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Найдено 20 публикаций
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Статья
Bogomolov F. A., Tschinkel Y., Hassett B. Duke Mathematical Journal. 2011. Vol. 157. No. 3. P. 535-550.
Добавлено: 23 июня 2011
Статья
Rybnikov L. G., Halacheva I., Kamnitzer J. et al. Duke Mathematical Journal. 2020. Vol. Advanced publication. P. 1-83.
Добавлено: 22 июля 2020
Статья
Voisin C., Amerik E. Duke Mathematical Journal. 2008. No. 145(2). P. 379-408.
Добавлено: 17 октября 2011
Статья
Losev Ivan. Duke Mathematical Journal. 2017. Vol. 166. No. 1. P. 27-73.
Добавлено: 15 октября 2017
Статья
Gorodentsev A. L., Rudakov A. N. Duke Mathematical Journal. 1987. Vol. 54. No. 1. P. 115-130.
Добавлено: 5 мая 2010
Статья
Arzhantsev I., Flenner H., Kaliman S. et al. Duke Mathematical Journal. 2013. Vol. 162. No. 4. P. 767-823.
Добавлено: 24 марта 2013
Статья
Galkin S., Golyshev V., Iritani H. Duke Mathematical Journal. 2016. Vol. 165. No. 11. P. 2005-2077.

We propose Gamma Conjectures for Fano manifolds which can be thought of as a square root of the index theorem. Studying the exponential asymptotics of solutions to the quantum differential equation, we associate a principal asymptotic class A_F to a Fano manifold F. We say that F satisfies Gamma Conjecture I if A_F equals the Gamma class Γ_F. When the quantum cohomology of F is semisimple, we say that F satisfies Gamma Conjecture II if the columns of the central connection matrix of the quantum cohomology are formed by Γ_F Ch(E_i) for an exceptional collection {E_i} in the derived category of coherent sheaves D^b_{coh}(F). Gamma Conjecture II refines part (3) of Dubrovin's conjecture. We prove Gamma Conjectures for projective spaces, toric manifolds, certain toric complete intersections and Grassmannians.

Добавлено: 18 ноября 2014
Статья
Khoroshkin A., Dotsenko V. Duke Mathematical Journal. 2010. Vol. 153. No. 2. P. 363-396.

It is now well-known that applications of the operad theory in general (and, in particular, to verifications of the Koszul property) are really difficult in particular computations. There was no known ``arithmetic'' of operations similar to the arithmetic of integers or polynomials (by an ``arithmetic'' we mean the usual notion of divisibility). The good analogue of multiplication for the operadic data is the composition of operations. But the action of the symmetric groups on the entries of operations contradicts with any possible functorial definition of divisibility. This paper contains a solution to this problem using the notion of Shuffle operads. The key idea is to forget about a certain part of the action of the symmetric group. In spite of being a very simple idea, it allowed us to introduce a theory of monomials, their divisibility and compatible orderings of monomials for operads. Summarizing these notions, we came up with the notion of Grobner bases for operads. Grobner bases is a remarkable technical tool initiated in the commutative algebra setting by Buchberger which allows one to solve systems of equations with many unknowns. The theory of Grobner bases for operads made it possible to provide a unified proof of the existing computational results in the field as well as to prove some new results. It is clear that there are many topics that can be successfully approached by these new methods.

Добавлено: 29 сентября 2013
Статья
Feigin B. L., Felder G., Shoikhet B. Duke Mathematical Journal. 1995. Vol. 127. No. 3. P. 487-517.
Добавлено: 28 мая 2010
Статья
Krichever I. M., Grushevsky S. Duke Mathematical Journal. 2010. Vol. 152. No. 2. P. 317-371.
Добавлено: 17 апреля 2014
Статья
Athreya J., Bufetov A.I., Eskin A. et al. Duke Mathematical Journal. 2012. Vol. 161. No. 6. P. 1055-1111.

We apply some of the ideas of Margulis's Ph.D. dissertation to Teichmüller space. Let X be a point in Teichmüller space, and let B R.X/ be the ball of radius R centered at X (with distances measured in the Teichmüller metric). We obtain asymptotic formulas as R tends to infinity for the volume of B R.X/, and also for the cardinality of the intersection of B R.X/ with an orbit of the mapping class group.

Добавлено: 5 февраля 2013
Статья
Verbitsky M. Duke Mathematical Journal. 2013. Vol. 162. No. 15 (2013). P. 2929-2986.
Добавлено: 10 декабря 2013
Статья
Polishchuk A. Duke Mathematical Journal. 2017. Vol. 166. No. 15. P. 2871-2924.

We define and study the stack U^{ns,a}_{g,g} of (possibly singular) projective curves of arithmetic genus g with g smooth marked points forming an ample non-special divisor. We define an explicit closed embedding of a natural 𝔾gm-torsor over U^{ns,a}_{g,g} into an affine space and give explicit equations of the universal curve (away from characteristics 2 and 3). This construction can be viewed as a generalization of the Weierstrass cubic and the j-invariant of an elliptic curve to the case g>1. Our main result is that in characteristics different from 2 and 3 our moduli space of non-special curves is isomorphic to the moduli space of minimal A-infinity structures on a certain finite-dimensional graded associative algebra Eg (introduced in arXiv:1208.6332). We show how to compute explicitly the A-infinity structure associated with a curve (C,p1,...,pg) in terms of certain canonical generators of the algebra of functions on C−{p1,...,pg} and canonical formal parameters at the marked points. We study the GIT quotients associated with our representation of U^{ns,a}_{g,g} as the quotient of an affine scheme by 𝔾m^g and show that some of the corresponding stack quotients give modular compactifications of M_{g,g} in the sense of arXiv:0902.3690. We also consider an analogous picture for curves of arithmetic genus 0 with n marked points which gives a new presentation of the moduli space of ψ-stable curves (also known as Boggi-stable curves) and its interpretation in terms of A∞-structures.

Добавлено: 1 июля 2017
Статья
Feigin B. L., Rybnikov L. G., Frenkel E. Duke Mathematical Journal. 2010. Vol. 155. No. 2. P. 337-363.
"The universal enveloping algebra of any simple Lie algebra g contains a family of commutative subalgebras, called the quantum shift of argument subalgebras math.RT/0606380 , math.QA/0612798 . We prove that generically their action on finite-dimensional modules is diagonalizable and their joint spectra are in bijection with the set of monodromy-free opers for the Langlands dual group of G on the projective line with regular singularity at one point and irregular singularity of order two at another point. We also prove a multi-point generalization of this result, describing the spectra of commuting Hamiltonians in Gaudin models with irregular singulairity. In addition, we show that the quantum shift of argument subalgebra corresponding to a regular nilpotent element of g has a cyclic vector in any irreducible finite-dimensional g-module. As a byproduct, we obtain the structure of a Gorenstein ring on any such module. This fact may have geometric significance related to the intersection cohomology of Schubert varieties in the affine Grassmannian."
Добавлено: 12 октября 2012
Статья
Alexei Borodin, Bufetov A. Duke Mathematical Journal. 2014. Vol. 163. No. 11. P. 2109-2158.

Мы изучаем асимптотики следов (некоммутативных) мономов, которые формируются с помощью образов некоторых естественных элементов в универсальной обертывающей алгебре бесконечномерной унитарной группы в планшерелевском представлении. Мы доказываем, что эти мономы сходятся к моментам (коммутативного) гауссовского процесса, который можно определить как семейство нетривиально коррелированных двумерных гауссовских свободных полей. Этот предельный процесс ранее возникал как глобальный предел для спектра подматриц вигнеровских эрмитовых матриц.

Добавлено: 25 декабря 2014
Статья
Braverman A., Finkelberg M. V. Duke Mathematical Journal. 2010. Vol. 152. No. 1. P. 175-206.

This paper is the first in a series that describe a conjectural analog of the geometric Satake isomorphism for an affine Kac-Moody group (in this paper for simplicity we consider only untwisted and simply connected case). The usual geometric Satake isomorphism for a reductive group G identifies the tensor category Rep(G_) of finitedimensional representations of the Langlands dual group G_ with the tensor category PervG(O)(GrG) of G(O)-equivariant perverse sheaves on the affine Grassmannian GrG = G(K)/G(O) of G (here K = C((t)) and O = C[[t]]). As a byproduct one gets a description of the irreducible G(O)-equivariant intersection cohomology sheaves of the closures of G(O)-orbits in GrG in terms of q-analogs of the weight multiplicity for finite dimensional representations of G_. The purpose of this paper is to try to generalize the above results to the case when G is replaced by the corresponding affine Kac-Moody group Gaff (we shall refer to the (not yet constructed) affine Grassmannian of Gaff as the double affine Grassmannian). More precisely, in this paper we construct certain varieties that should be thought of as transversal slices to various Gaff(O)-orbits inside the closure of another Gaff (O)-orbit in GrGaff . We present a conjecture that computes the IC sheaf of these varieties in terms of the corresponding q-analog of the weight multiplicity for the Langlands dual affine group G_aff and we check this conjecture in a number of cases. Some further constructions (such as convolution of the corresponding perverse sheaves, analog of the Beilinson-Drinfeld Grassmannian etc.) will be addressed in another publication.

Добавлено: 12 октября 2012
Статья
Loktev S., Kedem R., Jimbo M. et al. Duke Mathematical Journal. 2004. Vol. 125. No. 3. P. 549-588.
Добавлено: 28 мая 2010
Статья
Bonatti C., Grines V., Pochinka O. Duke Mathematical Journal. 2019. Vol. 168. No. 13. P. 2507-2558.
Добавлено: 23 октября 2017
Статья
Eugene Gorsky, Oblomkov A., Rasmussen J. et al. Duke Mathematical Journal. 2014. Vol. 163. No. 14. P. 2709-2794.
Добавлено: 9 декабря 2014
Статья
Lunts V., Finkelberg M. V., Bressler P. Duke Mathematical Journal. 1990. Vol. 61. No. 3. P. 763-777.
Добавлено: 11 июня 2010