Rational surfaces and moduli spaces of vector bundles on rational surfaces |
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Authors: | L Costa R M Miró-Roig |
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Institution: | Dept. àlgebra i Geometria, Facultat de Matemàtiques, Universiat de Barcelona, 08007 Barcelona, Spain, e-mail: costa@mat.ub.es, e-mail: miro@mat.ub.es, ES
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Abstract: | Let X be a smooth algebraic surface, L ? Pic(X) L \in \textrm{Pic}(X) and H an ample divisor on X. Set MX,H(2; L, c2) the moduli space of rank 2, H-stable vector bundles F on X with det(F) = L and c2(F) = c2. In this paper, we show that the geometry of X and of MX,H(2; L, c2) are closely related. More precisely, we prove that for any ample divisor H on X and any L ? Pic(X) L \in \textrm{Pic}(X) , there exists
n0 ? \mathbbZ n_0 \in \mathbb{Z} such that for all
n0 \leqq c2 ? \mathbbZ n_0 \leqq c_2 \in \mathbb{Z} , MX,H(2; L, c2) is rational if and only if X is rational. |
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