Characteristic Classes of Hypersurfaces and Characteristic Cycles

Abstract

We give a new formula for the Chern-Schwartz-MacPherson class of a hypersurface in a nonsigular compact complex analytic variety. In particular this formula generalizes our previous result on the Euler characteristic of such a hypersurface. Two different approaches are presented. The first is based on the theory of characteristic cycle and the works of Sabbah, Briancon-Maisonobe-Merle, and Le-Mebkhout. In particular, this approach leads to a simple proof of a formula of Aluffi for the above mentioned class. The second approach uses Verdier's specialization property of the Chern-Schwartz-MacPherson classes. Some related new formulas are also given.

AMS-LaTeX, 15 pages

Cited by in corpus (32)

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• Categorification of Donaldson-Thomas invariants via Perverse Sheaves
• Characteristic classes of mixed Hodge modules
• Projective duality and a Chern-Mather involution
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• Positivity of Segre-MacPherson classes
• The local motivic DT/PT correspondence
• The Chern-Schwartz-MacPherson class of an embeddable scheme
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• Interpolation of characteristic classes of singular hypersurfaces
• Segre classes and invariants of singular varieties
• Refined invariants of finite-dimensional Jacobi algebras
• Chern classes of graph hypersurfaces and deletion-contraction
• Vanishing cohomology and Betti bounds for complex projective hypersurfaces
• Characteristic classes of complex hypersurfaces
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• Lê cycles and Milnor classes
• Towards a simple characterization of the Chern-Schwartz-MacPherson class
• Naive motivic Donaldson-Thomas type Hirzebruch classes and some problems
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• Motivic Milnor classes
• D-critical locus structure on the Hilbert schemes of some local toric Calabi-Yau threefolds
• On a relative form of Verdier Specialization
• On the explicit calculation of Hirzebruch-Milnor classes of hyperplane arrangements
• Hirzebruch-Milnor classes of complete intersections
• Calculations with Characteristic Cycles