TY - JOUR

T1 - On equivariant indices of 1-forms on varieties

AU - Gusein-Zade, Sabir M.

AU - Mamedova, Firuza

N1 - Funding information: ?The work of the first author (Secs. 1, 2, 5, and 6) was supported by a grant of the Russian Science Foundation (project no. 16-11-10018).

PY - 2017/7/1

Y1 - 2017/7/1

N2 - Given a G-invariant holomorphic 1-form with an isolated singular point on a germ of a complex-analytic G-variety with an isolated singular point (G is a finite group), its equivariant homological index and (reduced) equivariant radial index are defined as elements of the ring of complex representations of the group. We show that these indices coincide on a germ of a smooth complex analytic G-variety. This makes it possible to consider the difference between them as a version of the equivariant Milnor number of a germ of a G-variety with an isolated singular point.

AB - Given a G-invariant holomorphic 1-form with an isolated singular point on a germ of a complex-analytic G-variety with an isolated singular point (G is a finite group), its equivariant homological index and (reduced) equivariant radial index are defined as elements of the ring of complex representations of the group. We show that these indices coincide on a germ of a smooth complex analytic G-variety. This makes it possible to consider the difference between them as a version of the equivariant Milnor number of a germ of a G-variety with an isolated singular point.

UR - http://www.scopus.com/inward/record.url?scp=85029761503&partnerID=8YFLogxK

UR - https://arxiv.org/abs/1701.01827

U2 - 10.48550/arXiv.1701.01827

DO - 10.48550/arXiv.1701.01827

M3 - Article

AN - SCOPUS:85029761503

VL - 51

SP - 177

EP - 184

JO - Functional Analysis and its Applications

JF - Functional Analysis and its Applications

SN - 0016-2663

IS - 3

ER -