Self-duality of Coble's quartic hypersurface and applications
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The moduli space M0 of semi-stable rank 2 vector bundles with fixed trivial determinant over a non-hyperelliptic curve C of genus 3 is isomorphic to a quartic hypersurface in P 7 (Coble's quartic).Abstract:
The moduli space M0 of semi-stable rank 2 vector bundles with fixed trivial determinant over a non-hyperelliptic curve C of genus 3 is isomorphic to a quartic hypersurface in P 7 (Coble’s quartic). We show that M0 is self-dual and that its polar map associates to a stable bundle E ∈ M0 a bundle F which is characterized by dim H 0 (C, E ⊗ F) = 4. The projectiveread more
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Projectively Dual Varieties
TL;DR: In this paper, a review paper on projectively dual varieties is presented, which includes dual varieties, Pyasetskii pairing, discriminant complexes, resultants and schemes of zeros, secant and tangential varieties, Ein theorems, applications of projective differential geometry and Mori theory to dual varieties.
Book ChapterDOI
Moduli of Abelian Varieties, Vinberg θ-Groups, and Free Resolutions
TL;DR: In this article, a systematic approach to studying the geometric aspects of Vinberg θ-representations is presented, using the Borel-Weil construction for representations of reductive groups as sections of homogeneous bundles on homogeneous spaces, and then to study degeneracy loci of these vector bundles.
Journal ArticleDOI
Vector bundles and theta functions on curves of genus 2 and 3
TL;DR: In this paper, it was shown that the SIcir moduli space of vector bundles of rank r and trivial determinant on a smooth projective complex curve is a normal projective variety, which can be considered as a nonabelian analogue of the Jacobian variety JC.
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Vector bundles on curves and theta functions
TL;DR: In this paper, a survey lecture on the "theta map" from the moduli space of SL_r bundles on a curve C to the projective space of r-th order theta functions on JC is presented.
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Projective duality and a Chern-Mather involution
TL;DR: In this paper, the authors deduce the existence of an explicit involution on a part of the Chow group of projective space, encoding the effect of duality on Chern-Mather classes.
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Phillip Griffiths,Joe Harris +1 more
TL;DR: In this paper, a comprehensive, self-contained treatment of complex manifold theory is presented, focusing on results applicable to projective varieties, and including discussion of the theory of Riemann surfaces and algebraic curves, algebraic surfaces and the quadric line complex.
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Finn F. Knudsen,David Mumford +1 more
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Point sets in projective spaces and theta functions
David Ortland,Igor V. Dolgachev +1 more
TL;DR: In this paper, the authors present a collection of papers dedicated to L. Cayley's work on algebraic surfaces, including the following: A. COBLE, Algebraic geometry and theta functions, A. CAYLEY, A memoir on quartic surfaces.