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School Colloquium——Stable reduction of algebraic curves and abelian varieties
北大 algebraic curves abelian varieties
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2023/6/16
The stable reduction theorem was proved by Grothendieck for Abelian varieties and subsequently by Deligne and Mumford for projective curves.
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Number of rational points of difference varieties in finite difference fields
有限差分域 差分簇 有理点数
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2023/4/13
A difference field is a field with a distinguished automorphism. Automorphisms of a finite field are powers of the Frobenius map. In this talk, I will discuss how to estimate the number of rational po...
SCHUBERT POLYNOMIALS AND ARAKELOV THEORY OF ORTHOGONAL FLAG VARIETIES
SCHUBERT POLYNOMIALS ARAKELOV THEORY
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2015/12/17
We propose a theory of combinatorially explicit Schubert polynomials which represent the Schubert classes in the Borel presentation of the
cohomology ring of the orthogonal flag variety X = SON...
On representation varieties of Artin groups,projective arrangements and the fundamental groups of smooth complex algebraic varieties
Artin groups,projective arrangements fundamental groups smooth complex algebraic varieties
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2015/10/14
On representation varieties of Artin groups,projective arrangements and the fundamental groups of smooth complex algebraic varieties.
ABELIAN VARIETIES OVER LARGE ALGEBRAIC FIELDS WITH INFINITE TORSION
ABELIAN VARIETIES OVER LARGE ALGEBRAIC FIELDS INFINITE TORSION
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2015/8/26
Let A be a non-zero abelian variety defined over a number field K and let K be a fixed algebraic closure of K. For each element σ of the absolute Galois group Gal(K/K), let K(σ) be the fixed field in ...
The KH-Theory of Complete Simplicial Toric Varieties and the Algebraic K-Theory of Weighted Projective Spaces
Toric Varieties Algebraic K-Theory Weighted Projective Spaces K-regularity
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2012/7/11
We show that, for a complete simplicial toric variety $X$, we can determine its homotopy $\K$-theory (denoted $\KH$-theory) entirely in terms of the torus pieces of open sets forming an open cover of ...
Alexander varieties and largeness of finitely presented groups
Alexander varieties largeness of finitely presented groups Group Theory
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2012/5/9
Let X be a finite CW complex. We show that the fundamental group of X is large if and only if there is a finite cover Y of X and a sequence of finite abelian covers \{Y_N\} of Y which satisfy b_1(Y_N)...
On the Commuting variety of a reductive Lie algebra and other related varieties
polynomial algebra complex commuting variety desingularization Gorenstein Cohen-Macaulay rational singularities cohomology
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2012/4/18
In this note, one discusses about some varieties which are constructed analogously to the isospectral commuting varieties. These varieties are subvarieties of varieties having very simple desingulariz...
Handsaw quiver varieties and finite W-algebras
Handsaw quiver varieties finite W-algebras Quantum Algebra
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2011/9/20
Abstract: Following Braverman-Finkelberg-Feigin-Rybnikov (arXiv:1008.3655), we study the convolution algebra of a handsaw quiver variety, a.k.a. a parabolic Laumon space, and a finite W-algebra of typ...
On the Cohomology of Deligne-Lusztig Varieties
Cohomology of Deligne-Lusztig Varieties Representation Theory Group Theory
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2011/8/31
Abstract: In this paper, we present a conjecture on the degree of unipotent characters in the cohomology of particular Deligne-Lusztig varieties for groups of Lie type, and derive consequences of it. ...
Quantum analogues of Richardson varieties in the grassmannian and their toric degeneration
Quantum grassmannians quantum Richardson varieties quantum toric varieties straightening laws standard monomials
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2011/8/29
Abstract: In the present paper, we are interested in natural quantum analogues of Richardson varieties in the type A grassmannians. To be more precise, the objects that we investigate are quantum anal...
Tropical varieties with polynomial weights and corner loci of piecewise polynomials
Tropical varieties polynomial weights corner loci of piecewise polynomials
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2011/2/28
Counting Euler characteristics of the discriminant of the quadratic equation in terms of
Newton polytopes in two different ways, G. Gusev ([Gus]) found an unexpected relation for
mixed volumes of tw...
On certain varieties attached to a Weyl group element
certain varieties Weyl group element
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2011/1/20
0. Introduction and statement of results 0.1. Let k be an algebraically closed field. Let G be a connected reductive algebraic group over k. We assume that we are in one of the following two cases.(1)...
A note on the Frobenius morphism on toric varieties
note Frobenius morphism toric varieties
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2011/1/20
We give a new, shorter computation of Frobenius push-forwards of line bundles on toric varieties.
Categories of partial algebras for critical points between varieties of algebras
Partial algebra congruence relation gamp pregamp variety of algebras
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2011/1/19
We denote by Conc A the (∨, 0)-semilattice of all finitely generated congruences of an algebra A. A lifting of a (∨, 0)-semilattice S is an algebra A such that S ∼=Conc A.