Computing characteristic classes of projective schemes

Abstract

We discuss an algorithm computing the push-forward to projective space of several classes associated to a (possibly singular, reducible, nonreduced) projective scheme. For example, the algorithm yields the topological Euler characteristic of the support of a projective scheme $S$, given the homogeneous ideal of $S$. The algorithm has been implemented in Macaulay2.

15 pages. Code available at http://www.math.fsu.edu/~aluffi/CSM/CSM.html

References in corpus (3)

• Characteristic Classes of Hypersurfaces and Characteristic Cycles
• Chern classes for singular hypersurfaces
• A generalized Verdier-type Riemann-Roch theorem for Chern-Schwartz-MacPherson classes

Cited by in corpus (31)

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• Multidegrees of monomial rational maps
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• Newton-Okounkov bodies and Segre classes
• Computing the Chern-Schwartz-MacPherson Class of Complete Simplical Toric Varieties
• Applications of intersection theory: from maximum likelihood to chromatic polynomials
• Chern classes of logarithmic derivations for some non-free arrangements