Logarithmic Chow theory

Abstract

We describe a refined Chow theory for log schemes extending the theory of b-Chow suggested Holmes Pixton and Schmidt based off of a definition of Shokurov. This produces a dimension graded family of Abelian groups supporting a push-forward and pull-back along proper and log flat morphisms respectively, together with a bivariant theory satisfying Poincare Duality. In the final section we relate this construction to the construction of the log normal cone by Leo Herr.

References in corpus (4)

• Modification systems and integration in their Chow groups
• Stable logarithmic maps to Deligne--Faltings pairs II
• The Log Product Formula
• Semi-Perfect Obstruction theory and DT Invariants of Derived Objects

Cited by in corpus (3)

• Punctured logarithmic maps
• A case study of intersections on blowups of the moduli of curves
• Logarithmic moduli of roots of line bundles on curves