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Segre Class Computation and Practical Applications
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abstract
Let $X \subset Y$ be closed (possibly singular) subschemes of a smooth projective toric variety $T$. We show how to compute the Segre class $s(X,Y)$ as a class in the Chow group of $T$. Building on this, we give effective methods to compute intersection products in projective varieties, to determine algebraic multiplicity without working in local rings, and to test pairwise containment of subvarieties of $T$. Our methods may be implemented without using Groebner bases; in particular any algorithm to compute the number of solutions of a zero-dimensional polynomial system may be used.
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Cited by 1 Pith paper
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Spectral Decomposition of Euler-Mellin Integrals
Euler-Mellin integrals are shown to have their D-module characteristic variety and characteristic cycle computed by explicit blow-up or Whitney stratification recipes, giving Landau singularities.
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