Extensions of stable rank-3 vector bundles on ruled surface

HKUST Electronic Theses

Extensions of stable rank-3 vector bundles on ruled surface

by Chun-Lin Fan

THESIS 2004

M.Phil. Mathematics

vii, 21 leaves ; 30 cm

Abstract
In this thesis we study the M_H (3; 0, c₂) i.e the moduli space of H-stable rank-3 vector bundles V on ruled surface with the first and second Chern classes 0 and c₂ respectively. For a suitable ample divisor H, if the moduli space M_H (3; 0, c₂) is nonempty and c₂ = 3(n + _X( O_x) ) - 1 and c₂ > -9_X(O_x), then the generic bundle V ∈ M_H (3; 0, c₂) sits in the following short exact sequences

0 → O_x(-nf) → V → W → 0

and

0 → O_x(-nf) → V* → U → 0

where W and U are H-stable rank-2 vector bundles.

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Details

Collection HKUST Electronic Theses Degree M.Phil. Department Mathematics Authors Fan, Chun-Lin Subjects Moduli theory Surfaces, Algebraic Vector bundles Language English Call number Thesis MATH 2004 Fan DOI 10.14711/thesis-b832308

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Extensions of stable rank-3 vector bundles on ruled surface

by Chun-Lin Fan

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