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Everything about Segre class

In mathematics, the Segre class is a characteristic class used in the study of cones, a generalization of vector bundles. For vector bundles the total Segre class is inverse to the total Chern class, and thus provides equivalent information; the advantage of the Segre class is that it generalizes to more general cones, while the Chern class does not. The Segre class was introduced in the non-singular case by Beniamino Segre (1953). In the modern treatment of intersection theory in algebraic geometry, as developed e.g. in the definitive book of Fulton (1998), Segre classes play a fundamental role. Wikipedia →

🧭 Start here: a 6-step reading path

  1. Read the overview: Segre classA 5-minute orientation
  2. Skim a recent paper: Lorentzian polynomials, Segre classes, and adjoint polynomials of convex polyhedral conesInfluential work since 2022
  3. Pick up a classic book: Weber, Mosca, ParetoThe most-reprinted book on the subject
  4. Read the landmark paper: Algorithms to compute the topological Euler characteristic, Chern–Schwartz–MacPherson class and Segre class of projective varietiesCited 20 times
  5. Go sideways: Residual intersectionA closely related topic
  6. Go sideways: Pontryagin classA closely related topic

đź“– Definitions

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🗂️ The subject at a glance

  1. Definition
  2. Properties
  3. Examples
  4. Multiplicity along a subvariety

🏆 Landmark papers (most cited)

🆕 Influential since 2022

đź“š Books worth reading

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