Indices of Vector Fields and 1-Forms on Singular Varieties

Ebeling, Wolfgang; Guseĭn-Zade, S. M.

doi:10.1007/3-540-35480-8_4

Cited by 20 publications

(21 citation statements)

References 61 publications

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“…All the defined indices (as well as the radial one and the local Euler obstruction) satisfy the law of conservation of number (see, e.g., [5]). …”

Section: Propositionmentioning

confidence: 99%

“…The GSV (Gómez-Mont-Seade-Verjovsky) index or PH (Poincaré-Hopf) index is defined for isolated complete intersection singularities: ICIS. For definitions and properties of these indices see [5] and the references there. This paper emerged from an attempt to generalize the notion(s) of the GSV-or PH-indices from complete intersections to more general varieties.…”

Section: Introductionmentioning

confidence: 99%

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On indices of 1-forms on determinantal singularities

Guseĭn-Zade

Ebeling

2009

Proc. Steklov Inst. Math.

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We consider 1-forms on, so called, essentially isolated determinantal singularities (a natural generalization of isolated ones), show how to define analogues of the Poincaré-Hopf index for them, and describe relations between these indices and the radial index. For isolated determinantal singularities, we discuss properties of the homological index of a holomorphic 1-form and its relation with the Poincaré-Hopf index.

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“…All the defined indices (as well as the radial one and the local Euler obstruction) satisfy the law of conservation of number (see, e.g., [5]). …”

Section: Propositionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

On indices of 1-forms on determinantal singularities

Guseĭn-Zade

Ebeling

2009

Proc. Steklov Inst. Math.

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“…(For non-singular varieties both sets of characteristic numbers coincide with the usual Chern numbers.) A survey of these and adjacent results can be found in [5].…”

Section: Introductionmentioning

confidence: 99%

Indices of collections of equivariant 1-forms and characteristic numbers

Ebeling

Guseĭn-Zade

2015

Topology and its Applications

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If two G-manifolds are G-cobordant then characteristic numbers corresponding to the fixed point sets (submanifolds) of subgroups of G and to normal bundles to these sets coincide. We construct two analogues of these characteristic numbers for singular complex G-varieties where G is a finite group. They are defined as sums of certain indices of collections of 1-forms (with values in the spaces of the irreducible representations of subgroups). These indices are generalizations of the GSV-index (for isolated complete intersection singularities) and the Euler obstruction respectively.

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“…In the case that we have just one 1-form, the Chern number is the Euler obstruction of the differential form ( [6] p17). This is related to the Euler obstruction of a set and the Euler obstruction of a function as defined by Brasselet, Massey, Parameswaran and Seade in [4].…”

Section: Introductionmentioning

confidence: 99%