Projective duality and a Chern-Mather involution

Aluffi, Paolo

doi:10.1090/tran/7042

Projective duality and a Chern-Mather involution
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Trans. Amer. Math. Soc. 370 (2018), 1803-1822 Request permission

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 Plücker 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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