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Segre Classes and Invariants of Singular Varieties

In: Handbook of Geometry and Topology of Singularities III

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  • Paolo Aluffi

    (Florida State University, Math Dept.)

Abstract

Segre classes encode essential intersection-theoretic information concerning vector bundles and embeddings of schemes. In this paper we survey a range of applications of Segre classes to the definition and study of invariants of singular spaces. We will focus on several numerical invariants, on different notions of characteristic classes for singular varieties, and on classes of Lê cycles. We precede the main discussion with a review of relevant background notions in algebraic geometry and intersection theory.

Suggested Citation

  • Paolo Aluffi, 2022. "Segre Classes and Invariants of Singular Varieties," Springer Books, in: José Luis Cisneros-Molina & Lê Dũng Tráng & José Seade (ed.), Handbook of Geometry and Topology of Singularities III, chapter 0, pages 419-492, Springer.
    • Handle: RePEc:spr:sprchp:978-3-030-95760-5_6
    DOI: 10.1007/978-3-030-95760-5_6
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