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Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：关于仿射Deligne-Lusztig簇的研究
仿射 Deligne-Lusztig簇 仿射旗流形 几何性质 算术几何
2023/4/26
仿射Deligne-Lusztig簇是经典的Deligne-Lusztig簇在仿射旗流形中的类比，其几何性质在算术几何中有着重要的应用。本报告将介绍仿射Deligne-Lusztig簇与组合、算术几何、表示论等领域的联系，最新的进展,和一些公开问题。
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：On Deligne-Beilinson cohomology of the universal K3 surface
泛K3曲面 Deligne-Beilinson 同调
2023/5/15
O'Grady's generalized Franchetta conjecture is concerned with algebraic cycles of codimension 2 on the universal polarized K3 surface of genus g. This conjecture has been confirmed only for certain sm...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Some geometry of affine Deligne-Lusztig varieties
仿射 Deligne-Lusztig变种 几何
2023/5/17
The mod p points of a Shimura variety have a conjectural description called the Langlands-Rapoport conjecture. In accordance with the conjecture, Rapoport defined (generalized) affine Deligne-Lusztig ...
DELIGNE PAIRINGS AND FAMILIES OF RANK ONE LOCAL SYSTEMS ON ALGEBRAIC CURVES
DELIGNE PAIRINGS LOCAL SYSTEMS ALGEBRAIC CURVES
2015/12/17
For smooth families of projective algebraic curves, we extend the notion of intersection pairing of metrized line bundles to a pairing on line bundles with flat relative connections. In this setting, ...
Affine Deligne-Lusztig varieties in affine flag varieties
Affine Deligne-Lusztig flag varieties
2015/9/29
This paper studies ane Deligne-Lusztig varieties in the ane
ag manifold of a split
group. Among other things, it proves emptiness for certain of these varieties, relates
some of them to those fo...
AN ANALYTIC CONSTRUCTION OF THE DELIGNE-MUMFORD COMPACTIFICATION OF THE MODULI SPACE OF CURVES
ANALYTIC CONSTRUCTION DELIGNE-MUMFORD COMPACTIFICATION MODULI SPACE OF CURVES
2015/8/26
In 1969, P. Deligne and D. Mumford compactified the modulispace of curves Mg,n. Their compactification Mg,n is a projective algebraic variety, and as such, it has an underlying analytic structure. Alt...
On Spineless Cacti, Deligne's Conjecture and Connes--Kreimer's Hopf Algebra
Spineless Cacti Deligne's Conjecture Connes--Kreimer's Hopf Algebra
2015/3/25
Using a cell model for the little discs operad in terms of spineless cacti we give a minimal common topological operadic formalism for three a priori disparate algebraic structures: (1) a solution to ...
Deformations of algebras over operads and Deligne's conjecture
algebras over operads Deligne's conjecture
2015/3/25
In present paper we develop the deformation theory of operads and algebras over operads. Free resolutions (constructed via Boardman-Vogt approach) are used in order to describe formal moduli spaces of...
Manin products, Koszul duality, Loday algebras and Deligne conjecture
Manin products Koszul duality Loday algebras Deligne conjecture
2015/3/25
In this article we give a conceptual definition of Manin products in any category endowed with two coherent monoidal products. This construction can be applied to associative algebras, non-symmetric o...
Toric Deligne-Mumford stacks and the better behaved version of the GKZ hypergeometric system
Toric Deligne-Mumford stacks GKZ hypergeometric system Algebraic Geometry
2012/5/9
We generalize the combinatorial description of the orbifold (Chen--Ruan) cohomology and of the Grothendieck ring of a Deligne--Mumford toric stack and its associated stacky fan in a lattice $N$ in the...
Torelli theorem for the Deligne--Hitchin moduli space, II
Principal bundle Deligne–Hitchin moduli space Higgs bundle vector field
2012/3/1
Let X and X' be compact Riemann surfaces of genus at least three. Let G and G' be nontrivial connected semisimple linear algebraic groups over C. If some components $M_{DH}^d(X,G)$ and $M_{DH}^{d'}(X'...
On the Cohomology of Deligne-Lusztig Varieties
Cohomology of Deligne-Lusztig Varieties Representation Theory Group Theory
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. ...
Quivers of sections on toric Deligne-Mumford stacks
Quivers of sections toric Deligne-Mumford stacks
2011/1/21
Starting from a collection of line bundles on a smooth projective toric DM stack,we give a stacky analogue of the classical linear series construction. We apply our construction to recover the finite ...
The symplectic Deligne-Mumford stack associated to a stacky polytope
symplectic Deligne-Mumford stack stacky polytope
2010/12/8
We discuss a symplectic counterpart of the theory of stacky fans. First, we define a stacky
polytope and construct the symplectic toric Deligne–Mumford stack associated to it. Then we establish a rel...