IJPAM: Volume 10, No. 4 (2004)

MINIMAL FREE RESOLUTIONS AND SHEAVES
ON A CERTAIN INFINITE-DIMENSIONAL
COMPLEX PROJECTIVE SPACE

E. Ballico
Department of Mathematics
University of Trento
380 50 Povo (Trento) - Via Sommarive, 14, ITALY
e-mail: ballico@science.unitn.it


Abstract.Let $V$ be a locally convex complex topological vector space and $\mathcal {F}$ an $\mathcal {0}_{{\bf {P}}(V)}$-sheaf on ${\bf {P}}(V)$. Here we discuss the notion of minimal finite free resolution of $\mathcal {F}$. Assume $V:= {\bf {C}}^{{\bf {N}}}$ and let $X \subset {\bf {P}}(V)$ be a closed finitely determined analytic subset of ${\bf {P}}(V)$. Here we prove that the ideal sheaf of $X$ has a minimal free resolution.

Received: November 25, 2003

AMS Subject Classification: 30F99, 32K05, 32L05, 14H60

Key Words and Phrases: syzygy, minimal free resolution, holomorphic line bundle, infinite-dimensional complex projective space

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2004
Volume: 10
Issue: 4