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Эта публикация цитируется в 2 научных статьях (всего в 2 статьях)
Chern–Dold character in complex cobordisms and theta divisors
V. M. Buchstabera, A. P. Veselovb a Steklov Mathematical Institute and Moscow State University, Russia
b Department of Mathematical Sciences, Loughborough University, Loughborough LE11 3TU, UK
Аннотация:
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.
Поступила в редакцию: 06.03.2023 Исправленный вариант: 13.03.2024 Принята в печать: 04.05.2024
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