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Working paper

We propose a simple quality-ladder model with heterogeneous agents differing in their skills and wealth endowment to explain the persistence of barriers to entry in new democracies. In the model agents vote for a rate of redistribution and for the level of barriers to entry, which protect the incumbent firms from competition with new entrants. We show that even if a society democratizes, under certain conditions this leads only to the rise of redistribution, rather than to the elimination of barriers to entry. We show that this argument is particularly relevant for countries with a low level of human capital and high inequality in incomes and in skills.

Added: Feb 3, 2015

Working paper

Ballet S.,

math. arxive. Cornell University, 2017
We obtain new uniform bounds for the symmetric tensor rank of multiplication in finite extensions of any finite field Fp or Fp2 where p denotes a prime number greater or equal than 5. In this aim, we use the symmetric Chudnovsky-type generalized algorithm applied on sufficiently dense families of modular curves defined over Fp2 attaining the Drinfeld-Vladuts bound and on the descent of these families to the definition field Fp. These families are obtained thanks to prime number density theorems of type Hoheisel, in particular a result due to Dudek (2016).

Added: Jul 11, 2017

Working paper

The paper is dedicated to organizational dependence – independence of social enterprises (SEs) taking into account their multifaceted nature and complex business models shaping in line with the task of solving social problems at the crossroads of market, not-for-profit activity and state regulation. The paper is aimed at theoretical and empirical clarification of organizational nature of SEs on the basis of the international comparative study. We aimed to clarify the following issues: - To what extent the SEs in different countries (macro-regions) are oriented to the distinct forms of partnerships and do any of them have special bias to the state? - What factors play the main role in the character of a SE partnership (interactions) with stakeholders? - Do partnership forms relate to the level of independence of a SE from some bigger organizations or from the state? - Can we say that “independence” is most likely a characteristics of predominantly market oriented SEs (in terms of business model choice)? As the sampling frame of the survey we used the database of the fellows of Ashoka International network — the largest organization supported the leaders of social entrepreneurship worldwide. Respondents filled online a formalized questionnaire with 76 questions, and for the period from May through November, 2012 we received 128 questionnaires from 38 countries worldwide filled in English or Spanish. The subject of the research is social and economic activity of the SEs including strategy formation, assessment of condition of the target social groups, fundraising, partnership with other organizations, interactions with local and central governments, social, economic and institutional barriers of organizational activity. The data were processed with a SPSS package.

Added: Mar 29, 2015

Working paper

The paper is dedicated to organizational dependence – independence of social enterprises (SEs) taking into account their multifaceted nature and complex business models shaping in line with the task of solving social problems at the crossroads of market, not-for-profit activity and state regulation

Added: Dec 3, 2013

Working paper

Here are considered the conditions under which the method of diagrams is liable to include non-classical logics, among which the spatial representation of non-bivalent negation. This will be done with two intended purposes, namely: to review the basic concepts involved in the definition of logical negation; to account for a variety of epistemological obstacles against the introduction of non-classical negations within diagrammatic logic. It will be mainly argued that non-classical logics don't challenge dichotomy as such but merely show that a logical operator may be a negation without operating as a dichotomy.

Added: Nov 4, 2014

Working paper

We analyze whether a depositor’s familiarity with a bank affects depositor behavior during a financial crisis. Familiarity is measured by the presence of regional or local cues in the bank’s name, while depositor behavior is considered in terms of depositor sensitivity to observable bank risk (market discipline exerted by depositors). Using the 2001–2010 bank-level and region-level data for Russia, we show the evidence that depositors use quantity-based discipline on all banks in the sample. The evidence of a price-based discipline mechanism, however, is virtually absent. We find that depositors of familiar banks were less sensitive to bank risk after a financial crisis than depositors at unfamiliar banks. To assure the results are driven by familiarity bias and not implicit support of regional governments to banks with regional cues in their names, we interact the variables with measures of trust in local governments and regional affinity. We find a “flight to familiarity” effect strongly present in regions with strong regional affinity, while the effect is rejected in regions with greater trust in regional and local governments. This suggests that the results are driven by familiarity rather than implicit protection from trusted regional or local governments.

Added: Feb 4, 2017

Working paper

We analyse whether depositor familiarity with a bank affects depositor behaviour during a financial crisis. We measure familiarity by looking for regional or local cues in the bank’s name. We measure depositor behaviour by the their sensitivity to observable bank risk (market discipline). Using 2001–2010 bank-level and region-level data for Russia, we find that depositors of familiar banks become less sensitive to bank risk after a financial crisis relative to depositors of unfamiliar banks. To check that the results are not driven by any implicit support of banks with regional cues in their names by regional governments, but indeed by familiarity bias, we interact the variables of interest with measures of trust in local governments and regional affinity. We find that the flight to familiarity effect is strongly present in regions with strong regional affinity, while the effect is rejected in regions with more trust in regional and local governments. This indicates our results are driven by familiarity and not by any implicit protection from a trusted regional or local government.

Added: Oct 20, 2016

Working paper

In the immediate aftermath of Russia’s 1998 crisis household depositors withdrew money from the insolvent and state-owned Sberbank, despite its unique protection by two explicit government guarantees and its reputation of a repository of trust. This was less the case in well-educated, older, more conservative and remote regions and more so in wealthy, entrepreneurial and central regions, enjoying more media freedom. Survey data confirm that access to free media like NTV turns depositors more vigilant about their banks. Well educated people’s better understanding turns them less likely to run on Sberbank but more likely to run on other banks.

Added: Nov 12, 2013

Working paper

This paper describes a group of derivational verbal suffixes in Abaza, a polysynthetic language belonging to the Northwest Caucasian family. For each suffix I propose a short description of its most remarkable features. In particular, I discuss the polysemy of the refactive and assertive markers and their interaction with the event structure of the verb. Other suffixes such as the putative and inferential markers are interesting due to their peculiar morphological behavior. The diversity of the discussed affixes is tentatively explained by the different pathways of their morphological and semantic development.

Added: Dec 14, 2018

Working paper

Added: Nov 26, 2015

Working paper

We construct a twist-closed enhancement of the derived category of coherent sheaves on a smooth compact complex-analytic manifold by means of DG-category of dbar-superconnections.

Added: Oct 30, 2013

Working paper

Alexeev V.,

arxiv.org. math. Cornell University, 2012
Added: Feb 6, 2013

Working paper

We prove that the derived category D(C) of a generic curve of genus greater than one embeds into the derived category D(M) of the moduli space M of rank two stable bundles on C with fixed determinant of odd degree.

Added: Apr 10, 2017

Working paper

Given a variety Y with a rectangular Lefschetz decomposition of its derived category, we consider a degree n cyclic cover X→Y ramified over a divisor Z⊂Y. We construct semiorthogonal decompositions of D^b(X) and D^b(Z) with distinguished components A_X and A_Z, and prove the equivariant category of A_X (with respect to an action of the n-th roots of unity) admits a semiorthogonal decomposition into n−1 copies of A_Z.

Added: Jan 30, 2015

Working paper

In this paper we study the derived categories of coherent sheaves on Grassmannians Gr(k,n), defined over the ring of integers. We prove that the category D^b(Gr(k,n)) has a semi-orthogonal decomposition, with components being full subcategories of the derived category of representations of GL_k. This in particular implies existence of a full exceptional collection, which is a refinement of Kapranov's collection \cite{Kap}, which was constructed over a field of characteristic zero.
We also describe the right dual semi-orthogonal decomposition which has a similar form, and its components are full subcategories of the derived category of representations of GL_{n−k}. The resulting equivalences between the components of the two decompositions are given by a version of Koszul duality for strict polynomial functors.
We also construct a tilting vector bundle on Gr(k,n). We show that its endomorphism algebra has two natural structures of a split quasi-hereditary algebra over Z, and we identify the objects of D^b(Gr(k,n)), which correspond to the standard and costandard modules in both structures.
All the results automatically extend to the case of arbitrary commutative base ring and the category of perfect complexes on the Grassmannian, by extension of scalars (base change).
Similar results over fields of arbitrary characteristic were obtained independently in \cite{BLVdB}, by different methods.

Added: Feb 2, 2015

Working paper

We study the derived categories of coherent sheaves on Gushel-Mukai varieties. In the derived category of such a variety, we isolate a special semiorthogonal component, which is a K3 or Enriques category according to whether the dimension of the variety is even or odd. We analyze the basic properties of this category using Hochschild homology, Hochschild cohomology, and the Grothendieck group. We study the K3 category of a Gushel-Mukai fourfold in more detail. Namely, we show that this category is equivalent to the derived category of a K3 surface for a certain codimension 1 family of rational fourfolds, and to the K3 category of a birational cubic fourfold for a certain codimension 3 family. The first of these results verifies a special case of a duality conjecture which we formulate. We discuss our results in the context of the rationality problem for Gushel-Mukai varieties, which was one of the main motivations for this work.

Added: May 29, 2016

Working paper

We develop an approach that allows to construct semiorthogonal decompositions of derived categories of surfaces with rational singularities with components equivalent to derived categories of local finite dimensional algebras. First, we discuss how a semiorthogonal decomposition of a resolution of singularities of a surface X may induce a semiorthogonal decomposition of X. In the case when Xhas cyclic quotient singularities, we introduce the condition of adherence for the components of the resolution that allows to identify the components of the induced decomposition with derived categories of explicit local finite dimensional algebras. Further, we present an obstruction in the Brauer group of X to the existence of such semiorthogonal decomposition, and show that in the presence of the obstruction a suitable modification of the adherence condition gives a semiorthogonal decomposition of the twisted derived category of X. We illustrate the theory by exhibiting a semiorthogonal decomposition for the untwisted or twisted derived category of any normal projective toric surface depending on whether its Weil divisor class group is torsion-free or not. Finally, we relate our results to the results of Kawamata based on iterated extensions of reflexive sheaves of rank 1 on X.

Added: Dec 3, 2018

Working paper

We discuss a relation between the structure of derived categories of smooth projective varieties and their birational properties. We suggest a possible definition of a birational invariant, the derived category analogue of the intermediate Jacobian, and discuss its possible applications to the geometry of prime Fano threefolds and cubic fourfolds.

Added: Nov 15, 2015

Working paper

We prove derived equivalence of Calabi–Yau threefolds constructed by Ito–Miura–Okawa– Ueda as an example of non-birational Calabi–Yau varieties whose difference in the Grothendieck ring of varieties is annihilated by the affine line.

Added: Dec 1, 2016

Working paper

In this paper we study derived equivalences for Symplectic reflection algebras. We establish a version of the derived localization theorem between categories of modules over Symplectic reflection algebras and categories of coherent sheaves over quantizations of Q-factorial terminalizations of the symplectic quotient singularities. To do this we construct a Procesi sheaf on the terminalization and show that the quantizations of the terminalization are simple sheaves of algebras. We will also sketch some applications: to the generalized Bernstein inequality and to perversity of wall crossing functors.

Added: Oct 9, 2017

Working paper

Following the approach of Haiden-Katzarkov-Kontsevich arXiv:1409.8611, to any homologically smooth graded gentle algebra A we associate a triple (Σ_A,Λ_A;η_A), where Σ_A is an oriented smooth surface with non-empty boundary, Λ_A is a set of stops on ∂Σ_A and η_A is a line field on Σ_A, such that the derived category of perfect dg-modules of A is equivalent to the partially wrapped Fukaya category of (Σ_A,Λ_A;η_A). Modifying arguments of Johnson and Kawazumi, we classify the orbit decomposition of the action of the (symplectic) mapping class group of Σ_A on the homotopy classes of line fields. As a result we obtain a sufficient criterion for homologically smooth graded gentle algebras to be derived equivalent. Our criterion uses numerical invariants generalizing those given by Avella-Alaminos-Geiss in math/0607348, as well as some other numerical invariants. As an application, we find many new cases when the AAG-invariants determine the derived Morita class. As another application, we establish some derived equivalences between the stacky nodal curves considered in arXiv:1705.06023.

Added: Dec 6, 2018