A DOLBEAULT ISOMORPHISM FOR COMPLETE INTERSECTIONS IN INFINITE-DIMENSIONAL PROJECTIVE SPACE

TitleA DOLBEAULT ISOMORPHISM FOR COMPLETE INTERSECTIONS IN INFINITE-DIMENSIONAL PROJECTIVE SPACE
Publication TypeJournal Article
Year of Publication2005
AuthorsKotzev B
JournalAnnuaire de l’Université de Sofia “St. Kliment Ohridski”. Faculté de Mathématiques et Informatique
Volume97
Keywordsinfinite-dimensional complex manifolds, projective manifolds, vanishing theorems
Abstract

We consider a complex submanifold $X$ of finite codimension in an infinite-dimensional complex projective space $P$ and a holomorphic vector bundle E over X. Given a covering $\mathcal{U}$ of X with Zariski open sets, we define a subcomplex $\mathcal{C}(X, E)$ of the Čech complex corresponding to the vector bundle E and the covering $\mathcal{U}$. For a special class of coverings $\mathcal{U}$, we prove that the complex $\mathcal{C}(X, E)$ is acyclic when X is a complete intersection and P admits smooth partitions of unity.

2000 MSC

main 32L20, secondary 58B99

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