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The Log Product Formula in quantum $K$-theory

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arxiv 2012.09379 v2 pith:XOVBS6QI submitted 2020-12-17 math.AG

You-Cheng Chou , Leo Herr , Yuan-Pin Lee This is my paper · ORCID
classification math.AG
keywords formulatheoryinvariantsproductproveclassesexpressingfunctorial
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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.

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  1. The log Grothendieck ring of varieties

    math.AG 2024-12 conditional novelty 8.0 of 10

    The log Grothendieck ring of varieties is K0(Var)[P]/(P^2+P[G_m]), and a log chi-y genus built from it is motivic even though log Hodge numbers are not.

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