Parabolic vector bundles and equivariant vector bundles

Details Parabolic vector bundles and equivariant vector bundles Parabolic vector bundles and equivariant vector bundles

2001-02-02

arxiv.org/abs/math/0102016v1

Mathematics

Algebraic Geometry

46 pages, 1 figure

Scientific paper

Given a complex manifold $X$, a normal crossing divisor $D\subset X$ whose irreducible components $D_1,...,D_s$ are smooth, and a choice of natural numbers $r=(r_1,...,r_s)$, we construct a manifold $X(D,\ur)$ with an action of a torus $\Gamma$ and we prove that some full subcategory of the category of $\Gamma$-equivariant vector bundles on $X(D,r)$ is equivalent to the category of parabolic vector bundles on $(X,D)$ in which the lengths of the filtrations over each irreducible component of $X$ are given by $r$. When $X$ is Kaehler, we study the Kaehler cone of $X(D,r)$ and the relation between the corresponding notions of slope-stability.

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