UC Berkeley

Commutative Algebra and Algebraic Geometry Seminar

October 29, 2013

939 Evans Hall

3:45PM: Zipping Tate resolutions and exterior coalgebras

Gunnar Floeystad

This is the general construction of how one may start from an arbitrary Tate resolution (an exact free complex) $T$ over the exterior algebra $E(V)$, zip it with (the dual of) $E(W)$ and get a complex of $S(V \otimes W^*)$-modules. For specific $T$ one obtains classical and newer pure resolutions.

5:00PM: Torus Equivariant Vector Bundles

Nathan Ilten

Klyachko has shown that there is an equivalence of categories between equivariant vector bundles on a toric variety X and collections of filtered vector spaces satisfying some compatibility conditions. I will discuss a generalization of this equivalence to the setting of T-equivariant vector bundles on a normal variety X endowed with an effective action of an algebraic torus T. Indeed, T-equivariant vector bundles on X correspond to collections of filtered vector bundles on a suitable quotient of X. This correspondence can be applied to show that torus equivariant bundles of low rank on projective space split.

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