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arXiv · 1605.09393

Tensored Segre classes

Paolo Aluffi
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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.

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Paolo Aluffi. 2016-05-30. Tensored Segre classes. https://doi.org/10.1016/j.jpaa.2016.09.016

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