Projective duality and a Chern-Mather involution
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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.References
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Additional Information
- Paolo Aluffi
- Affiliation: Department of Mathematics, Florida State University, Tallahassee, Florida 32306
- MR Author ID: 265422
- Email: aluffi@math.fsu.edu
- 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
- © Copyright 2017 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 370 (2018), 1803-1822
- MSC (2010): Primary 14C17, 14B05
- DOI: https://doi.org/10.1090/tran/7042
- MathSciNet review: 3739192