On the geometry of moduli spaces of coherent systems on algebraic curves

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dc.creatorBradlow, S.
dc.creatorGarcia-Prada, O.
dc.creatorMercat, V.
dc.creatorMuñoz, V.
dc.creatorNewstead, P.
dc.date2004-07-30
dc.date2006-08-02
dc.date.accessioned2026-07-07T06:38:42Z
dc.date.available2026-07-07T06:38:42Z
dc.descriptionLet $C$ be an algebraic curve of genus $g$. A coherent system on $C$ consists of a pair $(E,V)$, where $E$ is an algebraic vector bundle over $C$ of rank $n$ and degree $d$ and $V$ is a subspace of dimension $k$ of the space of sections of $E$. The stability of the coherent system depends on a parameter $α$. We study the geometry of the moduli space of coherent systems for different values of $α$ when $k\leq n$ and the variation of the moduli spaces when we vary $α$. As a consequence, for sufficiently large $α$, we compute the Picard groups and the first and second homotopy groups of the moduli spaces of coherent systems in almost all cases, describe the moduli space for the case $k=n-1$ explicitly, and give the Poincaré polynomials for the case $k=n-2$.
dc.description38 pages; v3. Appendix and new references added; v4. minor corrections, two added references; v5. final version, one typo corrected and one reference deleted
dc.identifierhttps://arxiv.org/abs/math/0407523
dc.identifierhttp://arxiv.org/abs/math/0407523
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/100831
dc.subjectAlgebraic Geometry
dc.subjectDifferential Geometry
dc.subject14D20; 14H51; 14H60
dc.titleOn the geometry of moduli spaces of coherent systems on algebraic curves
dc.typetext

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