The Log Product Formula in quantum $K$-theory

Abstract

We prove a formula expressing the $K$-theoretic log Gromov-Witten invariants of a product of log smooth varieties $V\times W$ in terms of the invariants of $V$ and $W$. The proof requires introducing log virtual fundamental classes in $K$-theory and verifying their various functorial properties. We introduce a log version of $K$-theory and prove the formula there as well.

21 pages, comments welcome! v2: 27 pages, example added distinguishing log Gysin map from ordinary one

References in corpus (1)

• K-theory and G-theory of derived algebraic stacks

Cited by in corpus (2)

• A case study of intersections on blowups of the moduli of curves
• Higher Genus Quantum $K$--theory