Tensored Segre classes

DOI10.1016/J.JPAA.2016.09.016zbMATH Open1355.14002arXiv1605.09393OpenAlexW2410443366WikidataQ60145507 ScholiaQ60145507MaRDI QIDQ503804

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Publication date: 23 January 2017

Published in: (Search for Journal in Brave)

Abstract: We study a class obtained from the Segre class $s(Z,Y)$ of an embedding of schemes by incorporating the datum of a line bundle on $Z$. This class satisfies basic properties analogous to the ordinary Segre class, but leads to remarkably simple formulas in standard intersection-theoretic situations such as excess or residual intersections. We prove a formula for the behavior of this class under linear joins, and use this formula to prove that a `Segre zeta function' associated with ideals generated by forms of the same degree is a rational function.

Full work available at URL: https://arxiv.org/abs/1605.09393

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