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Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：The Brauer-Manin obstruction on algebraic stacks
代数栈 Brauer-Manin阻塞 Hasse原理
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2023/11/29
The Brauer-Manin obstruction is an old topic in local-global principle of varieties. I will talk about Brauer-Manin obstruction on algebraic stacks and extend some classical results such as the exact ...
Tracking ‘marine heatwaves’ since 1950–and how the ‘blob’ stacks up
marine heatwaves blob stacks up
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2016/4/13
Unusually warm oceans can have widespread effects on marine ecosystems. Warm patches off the Pacific Northwest from 2013 to 2015, and a couple of years earlier in the Atlantic Ocean, affected everythi...
ESSENTIAL DIMENSION AND ALGEBRAIC STACKS
ESSENTIAL DIMENSION ALGEBRAIC STACKS
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2015/9/29
Essential dimension is a numerical invariant of an algebraic
group G introduced by J. Buhler and the second author to study the
complexity of G-torsors over a eld K. It has since been studied by se...
ESSENTIAL DIMENSION OF MODULI OF CURVES AND OTHER ALGEBRAIC STACKS (WITH AN APPENDIX BY NAJMUDDIN FAKHRUDDIN)
ESSENTIAL DIMENSION OTHER ALGEBRAIC STACKS
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2015/9/29
In this paper we consider questions of the following type.
Let k be a base eld and K=k be a eld extension. Given a geometric
object X over a eld K (e.g. a smooth curve of genus g) what is the
le...
Stacks associated to abelian tensor categories
Stacks tensor categories Algebraic Geometry
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2012/6/9
For an abelian tensor category a stack is constructed. As an application we show that our construction can be used to recover a quasi-compact separated scheme from the category of its quasi-coherent s...
Toric Deligne-Mumford stacks and the better behaved version of the GKZ hypergeometric system
Toric Deligne-Mumford stacks GKZ hypergeometric system Algebraic Geometry
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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...
Toric Stacks II: Intrinsic Characterization of Toric Stacks
Toric Stacks II fan stack moduli Algebraic Geometry
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2011/9/1
Abstract: The purpose of this paper and its prequel (Toric Stacks I) is to introduce and develop a theory of toric stacks which encompasses and extends the notions of toric stacks defined in [Laf02, B...
Toric Stacks I: The Theory of Stacky Fans
Toric Stacks I The Theory of Stacky Fans Algebraic Geometry
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2011/9/1
Abstract: The purpose of this paper and its sequel (Toric Stacks II) is to introduce and develop a theory of toric stacks which encompasses and extends the notions of toric stacks defined in [Laf02, B...
Quivers of sections on toric Deligne-Mumford stacks
Quivers of sections toric Deligne-Mumford stacks
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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 ...
Weakly proper moduli stacks of curves
Weakly proper moduli stacks of curves
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2011/1/17
This is the first in a projected series of three papers in which we construct the second flip in the log minimal model program for Mg. We introduce the notion of a weakly proper algebraic stack.
Partial desingularizations of good moduli spaces of Artin toric stacks
Partial desingularizations good moduli spaces of Artin toric stacks
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2011/1/19
Let X be an Artin stack with good moduli space X → M. We define the Reichstein transform of X relative to a closed substack C ⊂ X to be the complement of the strict transform of the saturation o...
Matrix factorizations and singularity categories for stacks
Matrix factorizations singularity categories for stacks
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2010/11/23
We study matrix factorizations of a section W of a line bundle on an algebraic stack. We relate the corresponding derived category (the category of D-branes of type B in the Landau-Ginzburg model with...
Representability of derived stacks
Representability of derived stacks math
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2010/11/15
Lurie's representability theorem gives necessary and sufficient conditions for a functor to be an almost finitely presented derived geometric stack. We establish several variants of Lurie's theorem, ...
Representation stacks, D-branes and noncommutative geometry
Representation stacks D-branes noncommutative geometry
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2010/12/13
n this note we prove that the spec(C)-points of the representation Artin-stack [repnR/PGLn] of n-dimensional representations of an affine C-algebra R correspond to C-algebra morphisms R - An where An ...
Derived Resolution Property for Stacks, Euler Classes and Applications
Derived Resolution Property for Stacks Euler Classes Applications
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2010/12/13
By resolving any perfect derived object over a Deligne-Mumford stack, we define its Euler class. We then apply it to define the Euler numbers for a smooth Calabi-Yau threefold in P4. These numbers are...