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Chern Classes of Splayed Intersections

Published online by Cambridge University Press:  20 November 2018

Paolo Aluffi  and
Eleonore Faber
Paolo Aluffi
Affiliation:
Mathematics Department, Florida State University, Tallahassee FL 32306, USA. e-mail: aluffi@math.fsu.edu
Eleonore Faber
Affiliation:
Department of Computer and Mathematical Sciences, University of Toronto at Scarborough, Toronto, ON M1A 1C4 Institut Mittag-Leffler, Auravägen 17, SE-182-60 Djursholm, Sweden. email: efaber@math.toronto.edu
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Abstract

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We generalize the Chern class relation for the transversal intersection of two nonsingular varieties to a relation for possibly singular varieties, under a splayedness assumption. We show that the relation for the Chern–Schwartz–MacPherson classes holds for two splayed hypersurfaces in a nonsingular variety, and under a strong splayedness assumption for more general subschemes. Moreover, the relation is shown to hold for the Chern–Fulton classes of any two splayed subschemes. The main tool is a formula for Segre classes of splayed subschemes. We also discuss the Chern class relation under the assumption that one of the varieties is a general very ample divisor.

Keywords

14C1714J17Splayed intersectionChern-Schwartz-MacPherson classChern-Fulton classsplayed blowupSegre class
Type
Research Article
Information
Canadian Journal of Mathematics , Volume 67 , Issue 6 , 01 December 2015 , pp. 1201 - 1218
Copyright
Copyright © Canadian Mathematical Society 2015

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