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    Mukai's program for curves on a K3 surface

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    Let C be a general element in the locus of curves in M_g lying on some K3 surface, where g is congruent to 3 mod 4 and greater than or equal to 15. Following Mukai's ideas, we show how to reconstruct the K3 surface as a Fourier-Mukai transform of a Brill-Noether locus of rank two vector bundles on C

    Geometry of Algebraic Curves

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    Grundlehren der mathematischen Wissenschaften 26

    Combinatorial and Algebro-Geometric cohomology classes on the Moduli Spaces of Curves

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    Given a compact Riemann surface C of genus g, n points on it, and n positive real numbers (2g−2+n> 0), Strebel’s theory of quadratic differentials [15] provides a canonical way of dissecting C into n polygons and assigning lengths to their sides. As Mumford first noticed, this can be used to give a combinatorial description of the moduli space Mg,n o
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