From: Brenda Sue Cook (brenda@math.missouri.edu)
Date: Fri Apr 25 2008 - 08:37:52 CDT
Master’s Presentation
Department of Mathematics
Yevgen Yampolskiy
(University of Missouri)
Equivariant Chow groups
of toric quotients
Abstract: Let $X$ be a simplicial toric variety with torus $T$
determined by a fan $\Sigma$.
Cox showed that $X$ can be constructed as a quotient of another
(simpler) toric variety $W$ with torus $T'$ by a group $G$ that arise
from an exact sequence
$$0\to G \to T' \to T \to 0$$
We apply Brion's representation of $A^T_*(X)$ to simplicial toric
varieties to derive a computational formula for equivariant Chow groups
$A_*^T(X)$, and use it to construct an explicit isomorphism between
$A_*^{T'}(W)\otimes Q$ and $A^T_*(X)\otimes Q=A_*^{ T'/G}(W/G)\otimes
Q$.
References:
David Cox, The homogeneous coordinate ring of a toric variety, 1993.
Michel Brion, Equivariant Chow groups for torus actions, 1997.
Tuesday, April 29
1:00 p.m.
312 Math Sciences
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