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Chern-Dold character in complex cobordisms and theta divisorsстатья
Статья опубликована в высокорейтинговом журнале
Статья опубликована в журнале из списка Web of Science и/или Scopus- Авторы: Buchstaber V.M., Veselov A.P.
- Журнал: Advances in Mathematics
- Том: 449
- Год издания: 2024
- Издательство: Academic Press
- Местоположение издательства: United States
- Номер статьи: 109720
- DOI: 10.1016/j.aim.2024.109720
- 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.
- Добавил в систему: Бухштабер Виктор Матвеевич