Algorithms to compute the topological Euler characteristic, Chern-Schwartz-MacPherson class and Segre class of projective varieties

DOI10.1016/j.jsc.2015.03.007zbMath1349.14028arXiv1402.2930OpenAlexW2094689345MaRDI QIDQ491251

Martin Helmer

Publication date: 24 August 2015

Published in: Journal of Symbolic Computation (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1402.2930

zbMATH Keywords

Euler characteristicSegre classcomputer algebraChern-Schwartz-MacPherson classcomputational intersection theory

Mathematics Subject Classification ID

Intersection theory, characteristic classes, intersection multiplicities in algebraic geometry (14C17)

Related Items (19)

Characteristic Classes ⋮ Segre Classes and Invariants of Singular Varieties ⋮ The Segre zeta function of an ideal ⋮ Computing the Chern–Schwartz–MacPherson Class of Complete Simplical Toric Varieties ⋮ On the Euler characteristic of a relative hypersurface ⋮ A relative Segre zeta function ⋮ Mixed multiplicities, Segre numbers and Segre classes ⋮ Feynman integral relations from parametric annihilators ⋮ Virtual classes for the working mathematician ⋮ Computing Segre classes in arbitrary projective varieties ⋮ A Macaulay2 package for computations with rational maps ⋮ The Euclidean distance degree of smooth complex projective varieties ⋮ THE CHERN–SCHWARTZ–MACPHERSON CLASS OF AN EMBEDDABLE SCHEME ⋮ Computing topological zeta functions of groups, algebras, and modules. II. ⋮ CharacteristicClasses ⋮ Segre class computation and practical applications ⋮ Computing characteristic classes and the topological Euler characteristic of complex projective schemes ⋮ Probabilistic Saturations and Alt’s Problem ⋮ A direct algorithm to compute the topological Euler characteristic and Chern-Schwartz-MacPherson class of projective complete intersection varieties

Uses Software

• Macaulay2
• PHCpack
• SageMath
• Bertini
• CSM-A

Cites Work

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• New orientifold weak coupling limits in F-theory
• D-brane deconstructions in IIB orientifolds
• Limits of Chow groups, and a new construction of Chern-Schwartz-MacPherson classes
• Chern classes for singular algebraic varieties
• Computing characteristic classes of projective schemes.
• Euler characteristics of general linear sections and polynomial Chern classes
• Chern classes for singular hypersurfaces
• Classes de Chern des intersections complètes locales
• Algorithm 795
• A METHOD TO COMPUTE SEGRE CLASSES OF SUBSCHEMES OF PROJECTIVE SPACE
• The Numerical Solution of Systems of Polynomials Arising in Engineering and Science
• Polar Cremona transformations.

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