Algebra Seminar: Cellular \bf{A}^1-Homology of Toric Varieties and Wonderful Model
About this Event
3620 South Vermont Avenue, Los Angeles, CA 90089
Haoyang Liu, UC Santa Barbara
Title: Cellular A^1-Homology of Toric Varieties and Wonderful Model
Abstract: In this talk, we explore the calculations of cellular A^1-homology for smooth toric varieties, an analog of classic cellular homology. We provide an explicit description of pure shellable cases and discuss the derivation of the (Milnor-Witt) motivic decomposition for these cases, inspired by classic results in real toric manifolds. Our approach expresses the resulting invariants in terms of the associated combinatorial data. Additionally, we present a similar comparison between complexes for the wonderful model of subspace arrangements in the sense of De Concini and Procesi. This is a joint work with Keyao Peng.
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