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Chern-Dold character in complex cobordisms and theta divisors

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posted on 2024-05-28, 14:26 authored by Victor Buchstaber, Alexander VeselovAlexander Veselov

We show that the smooth theta divisors of general principally polarised abelian varieties can be chosen as irreducible algebraic representatives of the coefficients of the Chern-Dold character in complex cobordisms and describe the action of the Landweber-Novikov operations on them. We introduce a quantisation of the complex cobordism theory with the dual Landweber-Novikov algebra as the deformation parameter space and show that the Chern-Dold character can be interpreted as the composition of quantisation and dequantisation maps.

Some smooth real-analytic representatives of the cobordism classes of theta divisors are described in terms of the classical Weierstrass elliptic functions. The link with the Milnor-Hirzebruch problem about possible characteristic numbers of irreducible algebraic varieties is discussed.

History

School

  • Science

Department

  • Mathematical Sciences

Published in

Advances in Mathematics

Volume

449

Issue

2024

Publisher

Elsevier

Version

  • VoR (Version of Record)

Rights holder

© The Authors

Publisher statement

This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/).

Acceptance date

2024-05-04

Publication date

2024-05-22

Copyright date

2024

ISSN

0001-8708

Language

  • en

Depositor

Prof Alexander Veselov. Deposit date: 20 May 2024

Article number

109720

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