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- W2950270159 abstract "Let $(A,m)$ be a local hypersurface with isolated singularity. We show that Hochster's theta pairing vanishes on elements that are {numerically equivalent to zero} in the Grothendieck group of $A$ under the mild assumption that $spec A$ admits a resolution of singularity. We also prove that when $dim A =3$, the Hochster's theta pairing is positive semidefinite. These results combine to show that the counter-example of Dutta-Hochster-McLaughlin to general vanishing of Serre's intersection multiplicity exists for any three dimensional isolated hypersurface singularity that is not a UFD and has a desingularization. Our method involves showing that theta gives a bivariant class for the morphism $spec A/m to spec A$. It also follows that if $A$ is three dimensional isolated hypersurface singularity that has a desingularization, the divisor class group of $A$ is finitely generated torsion-free." @default.
- W2950270159 created "2019-06-27" @default.
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- W2950270159 creator A5055630802 @default.
- W2950270159 date "2012-08-30" @default.
- W2950270159 modified "2023-09-24" @default.
- W2950270159 title "Hochster's theta pairing and numerical equivalence" @default.
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- W2950270159 doi "https://doi.org/10.48550/arxiv.1208.6083" @default.
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