Skip to content
DraconiticResearch
Search Sources API
194,226 studies31 sourcesUpdated 35 min ago
PreprintCC BY 4.0arXiv

Sn-equivariant L-classes of Cartesian powers of Witt spaces and the Hodge index conjecture for symmetric products

  • Mohammadali Aligholi
Open at sourcePDFDOICite

Abstract

For a compact oriented even-dimensional Witt pseudomanifold X, we compute the Sn-equivariant Banagl--Zagier L-classes of Xn in terms of the Goresky--MacPherson L-classes of X and the intersection cohomology Euler characteristic of X. This generalizes a theorem of Zagier for manifolds. Our approach is based on analyzing the equivariant structure of the signature operator of Xn using equivariant KK-theory and power operations in analytic K-homology. We establish an analytic K-homology analogue of Moonen's algebraic localization theorem by proving that the localized Chern character of the n-th power operation, evaluated at an n-cycle, agrees with the n-th homological Adams operation applied to the Chern character. As an application, we prove that the characteristic class Hodge index conjecture for singular varieties, formulated by Brasselet--Schürmann--Yokura, is preserved under taking symmetric products of complex projective varieties.

Related

  1. On bordism classes of symmetric products of surfaces
    Georgy Chernykh, Dmitry Gugnin
    arXivPreprintCC BY 4.0Full textGeometry & topologyarXiv
  2. L-classes of symmetric products: a homological formula
    Julia Semikina, Don Zagier
    arXivPreprintarXiv licenceFull textGeometry & topologyarXiv
  3. Symmetric 2-rigs: coexponentiability and cartesian closure
    Mathieu Anel, Marcelo Fiore, Nicola Gambino
    arXivPreprintCC BY 4.0Full textAlgebra & number theoryarXiv
  4. On k-limited domination: complexity and Cartesian products
    Aleksandra Tepeh
    arXivPreprintCC BY 4.0Full textCombinatorics & discrete mathematicsarXiv
  5. The Pairing-Hamiltonian property in Cartesian products of graphs
    Federico Romaniello
    arXivPreprintCC BY 4.0Full textCombinatorics & discrete mathematicsarXiv

Cite

BibTeXRIS
BibTeX
@misc{aligholi2026snequivariant,
  title = {{$S_n$-equivariant $L$-classes of Cartesian powers of Witt spaces and the Hodge index conjecture for symmetric products}},
  author = {Mohammadali Aligholi},
  howpublished = {arXiv},
  year = {2026},
  month = nov,
  doi = {10.48550/arxiv.2611.02577},
  eprint = {2611.02577},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2611.02577},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - S_n-equivariant L-classes of Cartesian powers of Witt spaces and the Hodge index conjecture for symmetric products
AU  - Mohammadali Aligholi
PY  - 2026
DA  - 2026/11/02
PB  - arXiv
DO  - 10.48550/arxiv.2611.02577
UR  - https://arxiv.org/abs/2611.02577
AB  - For a compact oriented even-dimensional Witt pseudomanifold X, we compute the S_n-equivariant Banagl--Zagier L-classes of X^n in terms of the Goresky--MacPherson L-classes of X and the intersection cohomology Euler characteristic of X. This generalizes a theorem of Zagier for manifolds. Our approach is based on analyzing the equivariant structure of the signature operator of X^n using equivariant KK-theory and power operations in analytic K-homology. We establish an analytic K-homology analogue of Moonen's algebraic localization theorem by proving that the localized Chern character of the n-th power operation, evaluated at an n-cycle, agrees with the n-th homological Adams operation applied to the Chern character. As an application, we prove that the characteristic class Hodge index conjecture for singular varieties, formulated by Brasselet--Schürmann--Yokura, is preserved under taking symmetric products of complex projective varieties.
ER  -