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Regular version of the site
Of all publications in the section: 13
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Article
Rudakov A. N. Journal fuer die reine und angewandte Mathematik. 1994. Vol. 453. P. 113-135.
Added: Oct 16, 2012
Article
Rovinsky M. Journal fuer die reine und angewandte Mathematik. 2007. No. 604. P. 159-186.
Added: Oct 11, 2011
Article
Polishchuk A., Lekili Y. Journal fuer die reine und angewandte Mathematik. 2019. Vol. 2019. No. 755. P. 151-189.

We show that a certain moduli space of minimal A∞-structures coincides with the modular compactification ℳ_{1,n}(n−1)of ℳ_{1,n} constructed by Smyth in [26]. In addition, we describe these moduli spaces and the universal curves over them by explicit equations, prove that they are normal and Gorenstein, show that their Picard groups have no torsion and that they have rational singularities if and only if n≤11.

Added: May 10, 2020
Article
Polishchuk A., Lekili Y. Journal fuer die reine und angewandte Mathematik. 2017.

We show that a certain moduli space of minimal A∞-structures coincides with the modular compactification ℳ_{1,n(n−1)} of ℳ_{1,n} constructed by Smyth in [26]. In addition, we describe these moduli spaces and the universal curves over them by explicit equations, prove that they are normal and Gorenstein, show that their Picard groups have no torsion and that they have rational singularities if and only if n≤11.

Added: Jul 1, 2017
Article
Kuznetsov A. Journal fuer die reine und angewandte Mathematik. 2017.
We discuss Calabi–Yau and fractional Calabi–Yau semiorthogonal components of derived categories of coherent sheaves on smooth projective varieties. The main result is a general construction of a fractional Calabi–Yau category from a rectangular Lefschetz decomposition and a spherical functor. We give many examples of applications of this construction and discuss some general properties of Calabi–Yau categories.
Added: Jun 15, 2017
Article
Kuznetsov A. Journal fuer die reine und angewandte Mathematik. 2019. Vol. 2019. No. 753. P. 239-267.

We discuss Calabi–Yau and fractional Calabi–Yau semiorthogonal components of derived categories of coherent sheaves on smooth projective varieties. The main result is a general construction of a fractional Calabi–Yau category from a rectangular Lefschetz decomposition and a spherical functor. We give many examples of applications of this construction and discuss some general properties of Calabi–Yau categories.

Added: Oct 11, 2019
Article
Mikhail Skopenkov, Bobenko A. Journal fuer die reine und angewandte Mathematik. 2016. Vol. 2016. No. 270. P. 217-250.

We develop linear discretization of complex analysis, originally introduced by R. Isaacs, J. Ferrand, R. Duffin, and C. Mercat. We prove convergence of discrete period matrices and discrete Abelian integrals to their continuous counterparts. We also prove a discrete counterpart of the Riemann–Roch theorem. The proofs use energy estimates inspired by electrical networks.

Added: Sep 26, 2014
Article
Kuznetsov A. Journal fuer die reine und angewandte Mathematik. 2015. Vol. 2015. No. 708. P. 213-243.

We define the normal Hochschild cohomology of an admissible subcategory of the derived category of coherent sheaves on a smooth projective variety $X$ --- a graded vector space which controls the restriction morphism from the Hochschild cohomology of $X$ to the Hochschild cohomology of the orthogonal complement of this admissible subcategory. When the subcategory is generated by an exceptional collection, we define its new invariant (the height) and show that the orthogonal to an exceptional collection of height $h$ in the derived category of a smooth projective variety $X$ has the same Hochschild cohomology as $X$ in degrees up to $h - 2$. We use this to describe the second Hochschild cohomology of quasiphantom categories in the derived categories of some surfaces of general type. We also give necessary and sufficient conditions of fullness of an exceptional collection in terms of its height and of its normal Hochschild cohomology.

Added: Dec 22, 2013
Article
Finkelberg M. V., Kuznetsov A. Journal fuer die reine und angewandte Mathematik. 2000. Vol. 529. P. 155-203.
Added: Oct 12, 2012
Article
Dunin-Barkowski P., Mulase M., Norbury P. et al. Journal fuer die reine und angewandte Mathematik. 2017. Vol. 2017. No. 726. P. 267-289.

We construct the quantum curve for the Gromov–Witten theory of the complex projective line.

Added: Mar 3, 2015
Article
Feigin E., Kato S., Makedonskyi I. Journal fuer die reine und angewandte Mathematik. 2020. Vol. 764. P. 181-216.

We study the non-symmetric Macdonald polynomials specialized at infinity from various points of view. First, we define a family of modules of the Iwahori algebra whose characters are equal to the non-symmetric Macdonald polynomials specialized at infinity. Second, we show that these modules are isomorphic to the dual spaces of sections of certain sheaves on the semi-infinite Schubert varieties. Third, we prove that the global versions of these modules are homologically dual to the level one affine Demazure modules for simply-laced Dynkin types except for type $E_8$

Added: Aug 12, 2020
Article
Kiritchenko V., Hornbostel J. Journal fuer die reine und angewandte Mathematik. 2011. No. 656. P. 59-85.

We establish a Schubert calculus for Bott-Samelson resolutions in the algebraic cobordism ring of a complete flag variety G/B. 

Added: Nov 17, 2012
Article
Ivan Cheltsov, Constantin Shramov. Journal fuer die reine und angewandte Mathematik. 2014. Vol. 689. P. 201-241.

We show that infinitely many Gorenstein weakly-exceptional quotient singularities exist in all dimensions, we prove a weak-exceptionality criterion for five-dimensional quotient singularities, and we find a sufficient condition for being weakly-exceptional for six-dimensional quotient singularities. The proof is naturally linked to various classical geometrical constructions related to subvarieties of small degree in projective spaces, in particular Bordiga surfaces and Bordiga threefolds.

Added: Oct 10, 2013