On characteristic classes of singular hypersurfaces and involutive symmetries of the Chow group

Fullwood, James

doi:10.5427/jsing.2016.14g

Cited by 3 publications

(3 citation statements)

References 11 publications

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“…It is somewhat remarkable that M (X) and µ O(X) (JX) are exchanged by the 'same' operation. Such involutions are not uncommon in the theory, see [27], [37]. The µ-class has applications to e.g., duality, and such applications can be formulated in terms of the Milnor class.…”

Section: Chern-mather Classesmentioning

confidence: 99%

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Segre classes and invariants of singular varieties

Aluffi¹

2021

Preprint

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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.

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Section: Chern-mather Classesmentioning

confidence: 99%

“…See [28] and [37] for further discussions of [27,Definition 3.2]. In particular, Callejas-Bedregal, Morgado, and Seade propose an alternative 'geometric' definition in [28] (Definition 1.3), which does agree with Massey's for M = P n .…”

Section: Lê Cyclesmentioning

confidence: 99%

Segre classes and invariants of singular varieties

Aluffi¹

2021

Preprint

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“…Remark 2. In [12] the author defined another class Λ(X) to fit in the 'wrong' formula originally proposed in [8].…”

Section: Involutions Of Chern Classesmentioning

confidence: 99%

Characteristic Classes of Homogeneous Essential Isolated Determinantal Varieties

Zhang¹

2020

Preprint

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The (homogeneous) Essentially Isolated Determinantal Variety is the natural generalization of generic determinantal variety, and is fundamental example to study non-isolated singularities. In this paper we study the characteristic classes on these varieties. We give explicit formulas of their Chern-Schwartz-MacPherson classes via standard Schubert calculus. As corollaries we obtain formulas for their (generic) sectional Euler characteristics, characteristic cycles and polar classes. In particular, when such variety is a hypersurfaces we compute its Milnor class and the Euler characteristics of the local Milnor fibers. We prove that for such recursive group orbit hypersurfaces the local Euler obstructions completely determine the Milnor classes.In general for reflective group orbits, on the other hand we propose an algorithm to compute their local Euler obstructions via the Chern-Schwartz-MacPherson classes of the orbits, which can be obtained directly from representation theory. This builds a bridge from representation theory of the group action to the singularity theory of the induced orbits.Theorem. When n ≥ 3, the Milnor classes are computed by.When k = C we let F n,i , F ∧ 2n,2i and F S n,i be the local Milnor fibers. We have the following equivalent description:

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Characteristic Classes of Homogeneous Essential Isolated Determinantal Varieties

Zhang¹

2022

jsing

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On characteristic classes of singular hypersurfaces and involutive symmetries of the Chow group

Cited by 3 publications

References 11 publications

Segre classes and invariants of singular varieties

Segre classes and invariants of singular varieties

Characteristic Classes of Homogeneous Essential Isolated Determinantal Varieties

Characteristic Classes of Homogeneous Essential Isolated Determinantal Varieties

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