The cone theorem and the vanishing of Chow cohomology

2020/01/31 by Dan Edidin, Edidin, Dan, Ryan Richey +1
Mathematics · #14C15 #14F43 #14M25 #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Algebraic structures and combinatorial models #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology

paper · pdf · doi:10.48550/arxiv.2002.00083

openalex publication_date 2020/01/31 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We show that a cone theorem for \mathbbA¹-homotopy invariant contravariant functors implies the vanishing of the positive degree part of the operational Chow cohomology rings of a large class of affine varieties. We also discuss how this vanishing relates to a number of questions about representing Chow cohomology classes of GIT quotients in terms of equivariant cycles.

Related

• The chow cohomology of affine toric varieties
• The intrinsic stable normal cone
• Chow theory of toric variety bundles
• Towards an Intersection Chow Cohomology Theory for GIT Quotients
• Gopakumar-Vafa Invariants and Macdonald Formula