On Isotopies and Homologies of Subvarieties of Toric Varieties

Описание

Перевод названия: ОБ И3ОТОПИЯХ И ГОМОЛОГИЯХ ПОДМНОГООБРАЗИЙ В ТОРИЧЕСКИХ МНОГООБРАЗИЯХ

Тип публикации: статья из журнала

Год издания: 2010

Идентификатор DOI: 10.1007/s11202-010-0078-4

Ключевые слова: homology group; toric variety; coboundary operator, coboundary operator, homology group, toric variety

Аннотация: In a",(n) we consider an algebraic surface Y and a finite collection of hypersurfaces S(i). Froissart's theorem states that if Y and S(i) are in general position in the projective compactification of a",(n) together with the hyperplane at infinity then for the homologies of Y \a(a) S(i) we have a special decomposition in terms of tПоказать полностьюhe homology of Y and all possible intersections of S(i) in Y. We prove the validity of this homological decomposition on assuming a weaker condition: there exists a smooth toric compactification of a",n in which Y and S(i) are in general position with all divisors at infinity. One of the key steps of the proof is the construction of an isotopy in Y leaving invariant all hypersurfaces Y a (c) S(k) with the exception of one Y a (c) S(i), which is shifted away from a given compact set. Moreover, we consider a purely toric version of the decomposition theorem, taking instead of an affine surface Y the complement of a surface in a compact toric variety to a collection of hypersurfaces in it.

Ссылки на полный текст

Издание

Журнал: SIBERIAN MATHEMATICAL JOURNAL

Выпуск журнала: Vol. 51, Is. 5

Номера страниц: 776-788

ISSN журнала: 00374466

Место издания: NEW YORK

Издатель: CONSULTANTS BUREAU/SPRINGER

Авторы

Вхождение в базы данных