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Projective duality and a Chern-Mather involution


Author: Paolo Aluffi
Journal: Trans. Amer. Math. Soc. 370 (2018), 1803-1822
MSC (2010): Primary 14C17, 14B05
DOI: https://doi.org/10.1090/tran/7042
Published electronically: November 22, 2017
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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 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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Additional Information

Paolo Aluffi
Affiliation: Department of Mathematics, Florida State University, Tallahassee, Florida 32306
Email: aluffi@math.fsu.edu

DOI: https://doi.org/10.1090/tran/7042
Received by editor(s): February 17, 2016
Received by editor(s) in revised form: June 8, 2016
Published electronically: November 22, 2017
Additional Notes: The author’s research was supported in part by the Simons Foundation and by NSA grant H98230-15-1-0027
Article copyright: © Copyright 2017 American Mathematical Society

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