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14-XX Algebraic geometry
14Hxx Curves
14H60 Vector bundles on curves and their moduli

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Indecomposable parabolic bundles

William Crawley-Boevey (2004)

Publications Mathématiques de l'IHÉS

We study the possible dimension vectors of indecomposable parabolic bundles on the projective line, and use our answer to solve the problem of characterizing those collections of conjugacy classes of n×n matrices for which one can find matrices in their closures whose product is equal to the identity matrix. Both answers depend on the root system of a Kac-Moody Lie algebra. Our proofs use Ringel’s theory of tubular algebras, work of Mihai on the existence of logarithmic connections, the Riemann-Hilbert...

Integrable systems and moduli spaces of rank two vector bundles on a non-hyperelliptic genus 3 curve

Pol Vanhaecke (2005)

Annales de l’institut Fourier

We use the methods that were developed by Adler and van Moerbeke to determine explicit equations for a certain moduli space, that was studied by Narasimhan and Ramanan. Stated briefly it is, for a fixed non-hyperelliptic Riemann surface $Γ$ of genus $3$ , the moduli space of semi-stable rank two bundles with trivial determinant on $Γ$ . They showed that it can be realized as a projective variety, more precisely as a quartic hypersurface of $ℙ^{7}$ , whose singular locus is the Kummer variety of $Γ$ . We first construct...

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