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 Events
USC
Mon 21 Jan 2019, 4:00pm
Algebraic Geometry Seminar
MATH 126
TBA
MATH 126
Mon 21 Jan 2019, 4:00pm-5:00pm

Abstract

 
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University of Alberta
Mon 28 Jan 2019, 4:00pm
Algebraic Geometry Seminar
MATH 126
Multiplicity-free products of Schubert divisors
MATH 126
Mon 28 Jan 2019, 4:00pm-5:00pm

Abstract

Let G/B be a flag variety over C, where G is a simple algebraic group
with a simply laced Dynkin diagram, and B is a Borel subgroup. The
Bruhat decomposition of G defines subvarieties of G/B called Schubert
subvarieties. The codimension 1 Schubert subvarieties are called
Schubert divisors. The Chow ring of G/B is generated as an abelian
group by the classes of all Schubert varieties, and is "almost"
generated as a ring by the classes of Schubert divisors. More
precisely, an integer multiple of each element of G/B can be written
as a polynomial in Schubert divisors with integer coefficients. In
particular, each product of Schubert divisors is a linear combination
of Schubert varieties with integer coefficients.

In the first part of my talk I am going to speak about the
coefficients of these linear combinations. In particular, I am going
to explain how to check if a coefficient of such a linear combination
is nonzero and if such a coefficient equals 1. In the second part
of my talk, I will say something about an application of my result,
namely, how it makes it possible estimate so-called canonical
dimension of flag varieties and groups over non-algebraically-closed
fields.
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UBC
Mon 4 Feb 2019, 4:00pm
Algebraic Geometry Seminar
MATH 126
Motivic classes of algebraic groups
MATH 126
Mon 4 Feb 2019, 4:00pm-5:00pm

Abstract

The Grothendieck ring of algebraic stacks was introduced by Ekedahl in 2009. It may be viewed as a localization of the more common Grothendieck ring of varieties. If G is a finite group, then the class {BG} of its classifying stack BG is equal to 1 in many cases, but there are examples for which {BG}\neq 1. When G is connected, {BG} has been computed in many cases in a long series of papers, and it always turned out that {BG}*{G}=1. We exhibit the first example of a connected group G for which {BG}*{G}\neq 1. As a consequence, we produce an infinite family of non-constant finite étale group schemes A such that {BA}\neq 1.
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University of Colorado
Mon 18 Mar 2019, 4:00pm
Algebraic Geometry Seminar
MATH 126
TBA
MATH 126
Mon 18 Mar 2019, 4:00pm-5:00pm

Abstract

 
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