• A
• A
• A
• ABC
• ABC
• ABC
• А
• А
• А
• А
• А
Regular version of the site
Of all publications in the section: 323
Sort:
by name
by year
Working paper
Gayfullin S. math. arxive. Cornell University, 2018. No. arXiv:1709.09237.
In 2007, Dubouloz introduced Danielewski varieties. Such varieties general- ize Danielewski surfaces and provide counterexamples to generalized Zariski cancellation problem in arbitrary dimension. In the present work we describe the automorphism group of a Danielewski variety. This result is a generalization of a description of automorphisms of Danielewski surfaces due to Makar-Limanov.
Working paper
Kurnosov N., Ясинский Е. math. arxive. Cornell University, 2018
We study groups of bimeromorphic and biholomorphic automorphisms of projective hyperkähler manifolds. Using an action of these groups on some non-positively curved space, we deduce many of their properties, including finite presentation, strong form of Tits' alternative and some structural results about groups consisting of transformations with infinite order.
Working paper
Shramov K., Przyjalkowski V. math. arxive. Cornell University, 2019
We show that smooth well formed weighted complete intersections have finite automorphism groups, with several obvious exceptions.
Working paper
Granin S., Maximov Y. math. arxive. Cornell University, 2015
Working paper
Loktev S., Kato S. math. arxive. Cornell University, 2017. No. 1712.03508.
We construct a filtration on integrable highest weight module of an affine Lie algebra whose adjoint graded quotient is a direct sum of global Weyl modules. We show that the graded multiplicity of each Weyl module there is given by a corresponding level-restricted Kostka polynomial. This leads to an interpretation of level-restricted Kostka polynomials as the graded dimension of the space of conformal coinvariants. In addition, as an application of the level one case of the main result, we realize global Weyl modules of current algebras of type ADE in terms of Schubert manifolds of thick affine Grassmanian, as predicted by Boris Feigin.
Working paper
Beklemishev L. D., Dmitrieva A., Makowsky J. math. arxive. Cornell University, 2020
We provide a variant of an axiomatization of elementary geometry based on logical axioms in the spirit of Huzita--Justin axioms for the Origami constructions. We isolate the fragments corresponding to natural classes of Origami constructions such as Pythagorean, Euclidean, and full Origami constructions. The sets of Origami constructible points for each of the classes of constructions provides the minimal model of the corresponding set of logical axioms. Our axiomatizations are based on Wu's axioms for orthogonal geometry and some modifications of Huzita--Justin axioms. We work out bi-interpretations between these logical theories and theories of fields as described in J.A. Makowsky (2018). Using a theorem of M. Ziegler (1982) which implies that the first order theory of Vieta fields is undecidable, we conclude that the first order theory of our axiomatization of Origami is also undecidable.
Working paper
Sheina K. math. arxive. Cornell University, 2020. No. 04348v1.
The basic automorphism group   of a Cartan foliation (M, F) is the quotient group of the automorphism group of (M, F) by the normal subgroup, which preserves every leaf invariant. For Cartan foliations covered by fibrations, we find sufficient conditions for the existence of a structure of a finite-dimensional Lie group in their basic automorphism groups. Estimates of the dimension of these groups are obtained. For some class of Cartan foliations with integrable an Ehresmann connection, a method for finding of basic automorphism groups is specified.
Working paper
Cheltsov I., Zhang K., Rubinstein Y. math. arxive. Cornell University, 2018
The purpose of this article is to develop techniques for estimating basis log canonical thresholds on logarithmic surfaces. To that end, we develop new local intersection estimates that imply log canonicity. Our main motivation and application is to show the existence of Kahler-Einstein edge metrics on all but finitely many families of asymptotically log del Pezzo surfaces, partially confirming a conjecture of two of us. In an appendix we show that the basis log canonical threshold of Fujita-Odaka coincides with the greatest lower Ricci bound invariant of Tian.
Working paper
Shramov K. math. arxive. Cornell University, 2019
We prove that a finite group acting by birational automorphisms of a non-trivial Severi-Brauer surface over a field of characteristic zero contains a normal abelian subgroup of index at most 3. Also, we find an explicit bound for orders of such finite groups in the case when the base field contains all roots of 1.
Working paper
Polishchuk A., Johnson D. math. arxive. Cornell University, 2018
We study birational projective models of M_2,2 obtained from the moduli space of curves with nonspecial divisors. We describe geometrically which singular curves appear in these models and show that one of them is obtained by blowing down the Weierstrass divisor in the moduli stack of Z-stable curves \bar{M}_2,2(Z) defined by Smyth. As a corollary, we prove projectivity of the coarse moduli space \bar{M}_2,2(Z).
Working paper
Prokhorov Y., Duncan A., Cheltsov I. et al. math. arxive. Cornell University, 2019
We study the complexity of birational self-maps of a projective threefold X by looking at the birational type of surfaces contracted. These surfaces are birational to the product of the projective line with a smooth projective curve. We prove that the genus of the curves occuring is unbounded if and only if X is birational to a conic bundle or a fibration into cubic surfaces. Similarly, we prove that the gonality of the curves is unbounded if and only if X is birational to a conic bundle.
Working paper
Shramov K., Prokhorov Y. math. arxive. Cornell University, 2019
We classify compact complex surfaces whose groups of bimeromorphic selfmaps have bounded finite subgroups. We also prove that the stabilizer of a point in the automorphism group of a compact complex surface of zero Kodaira dimension, as well as the stabilizer of a point in the automorphism group of an arbitrary compact Kaehler manifold of non-negative Kodaira dimension, always has bounded finite subgroups.
Working paper
Loginov K., Birkar C. math. arxive. Cornell University, 2020
In this paper we investigate non-rationality of divisors on 3-fold log Fano fibrations (X,B)→Z under mild conditions. We show that if D is a component of B with coefficient ≥t>0 which is contracted to a point on Z, then D is birational to ℙ^1×C where C is a smooth projective curve with gonality bounded depending only on t. Moreover, if t>1/2, then genus of C is bounded depending only on t.
Working paper
Penskoi A., Nadirashvili N. S., Berdnikov A. S. math. arxive. Cornell University, 2016
The known upper bounds for the multiplicities of the Laplace-Beltrami operator eigenvalues on the real projective plane are improved for the eigenvalues with even indexes. Upper bounds for Dirichlet, Neumann and Steklov eigenvalues on the real projective plane with holes are also provided.
Working paper
Smirnov E. math. arxive. Cornell University, 2007
The classical Ehresmann-Bruhat order describes the possible degenerations of a pair of flags in a finite-dimensional vector space V; or, equivalently, the closure of an orbit of the group GL(V) acting on the direct product of two full flag varieties.  We obtain a similar result for triples consisting of two subspaces and a partial flag in V; this is equivalent to describing the closure of a GL(V)-orbit in the product of two Grassmannians and one flag variety. We give a rank criterion to check whether such a triple can be degenerated to another one, and we classify the minimal degenerations. Our methods involve only elementary linear algebra and combinatorics of graphs (originating in Auslander-Reiten quivers).
Working paper
Bodzenta A., Bondal A. I. math. arxive. Cornell University, 2017
Given a relatively projective birational morphism f:X→Y of smooth algebraic spaces with dimension of fibers bounded by 1, we construct tilting relative (over Y) generators TX,f and SX,f in Db(X). We develop a piece of general theory of strict admissible lattice filtrations in triangulated categories and show that Db(X) has such a filtration L where the lattice is the set of all birational decompositions f:X→gZ→hY with smooth Z. The t-structures related to TX,f and SX,f are proved to be glued via filtrations left and right dual to L. We realise all such Z as the fine moduli spaces of simple quotients of OX in the heart of the t-structure for which SX,g is a relative projective generator over Y. This implements the program of interpreting relevant smooth contractions of X in terms of a suitable system of t-structures on Db(X).
Working paper
Perry A., Kuznetsov A. math. arxive. Cornell University, 2019
We introduce the notion of a categorical cone, which provides a categorification of the classical cone over a projective variety, and use our work on categorical joins to describe its behavior under homological projective duality. In particular, our construction provides well-behaved categorical resolutions of singular quadrics, which we use to obtain an explicit quadratic version of the main theorem of homological projective duality. As applications, we prove the duality conjecture for Gushel-Mukai varieties, and produce interesting examples of conifold transitions between noncommutative and honest Calabi-Yau threefolds.
Working paper
Kuznetsov A., Perry A. math. arxive. Cornell University, 2018
We introduce the notion of a categorical join, which can be thought of as a categorification of the classical join of two projective varieties. This notion is in the spirit of homological projective duality, which categorifies classical projective duality. Our main theorem says that the homological projective dual category of the categorical join is naturally equivalent to the categorical join of the homological projective dual categories. This categorifies the classical version of this assertion and has many applications, including a nonlinear version of the main theorem of homological projective duality.