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arXiv · 1601.05427

Projective duality and a Chern-Mather involution

Paolo Aluffi
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Abstract

We observe that linear relations among Chern-Mather classes of projective varieties are preserved by projective duality. We deduce the existence of an explicit involution on a part of the Chow group of projective space, encoding the effect of duality on Chern-Mather classes. Applications include Pl\"ucker formulae, constraints on self-dual varieties, generalizations to singular varieties of classical formulas for the degree of the dual and the dual defect, formulas for the Euclidean distance degree, and computations of Chern-Mather classes and local Euler obstructions for cones.

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Paolo Aluffi. 2016-01-20. Projective duality and a Chern-Mather involution. https://doi.org/10.1090/tran%2F7042

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