Results 11 to 20 of about 144 (120)
The curve of “Prym canonical” Gauss divisors on a Prym theta divisor [PDF]
Transactions of the American Mathematical Society, 2001 Summary: The Gauss linear system on the theta divisor of the Jacobian of a nonhyperelliptic curve has two striking properties: (1) the branch divisor of the Gauss map on the theta divisor is dual to the canonical model of the curve; (2) those divisors in the Gauss system parametrized by the canonical curve are reducible.
Smith, Roy, Varley, Robert
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ON THE THETA DIVISOR OF SU(2,1)
International Journal of Mathematics, 1999 Let SU(2,1) be the moduli space of stable rank two vector bundles having fixed determinant of odd degree over a compact Riemann surface C. In this paper it is shown that the Theta divisor of SU(2,1) is very ample for every C. The proof is related to the study of the base locus of the pencil of divisors 2-theta in the Jacobian of C which is naturally ...
Brivio S., Verra A.
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Singularities of $2\Theta $-divisors in the jacobian [PDF]
Bulletin de la Société mathématique de France, 2001 We study several subseries of the space of second order theta functions on the Jacobian of a non-hyperelliptic curve. In particular, we are interested in the subseries PΓ_{00} consisting of 2theta-divisors having multiplicity at least 4 at the origin, or, equivalently, containing the surface C-C, and in its analogues consisting of 2theta-divisors ...
Pauly, Christian, Previato, Emma
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Multiplicity g points on theta divisors
Duke Mathematical Journal, 1996 Let \((A,\Theta)\) be a principally polarized abelian variety of dimension \(g\). \(\text{Sing}_m (\Theta)\) denotes the subvariety of the theta divisor \(\Theta\) of points of multiplicity \(\geq m\). -- \textit{J. Kollár} [``Shafarevich maps and automorphic forms'' (Princeton 1995; Zbl 0871.14015)] showed that the dimension of \(\text{Sing}_m (\Theta)
Smith, Roy, Varley, Robert
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The Motive of a Smooth Theta Divisor
Documenta Mathematica, 2020 In this paper, we prove a motivic version of the Lefschetz hyperplane theorem for the motive a smooth ample divisor on an abelian variety.
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A theta divisor containing an abelian subvariety [PDF]
Pacific Journal of Mathematics, 2004 This short note by the late G. Kempf, which was originally going to be published in 1993, unfortunately got lost and is now recovered. The author constructs, over an algebraically closed field of characteristic zero, a three-dimensional Jacobian \(X\) whose theta divisor \(\theta\) contains an elliptic curve. The construction starts from two isogenies \
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Decomposable Theta Divisors and Generic Vanishing [PDF]
International Mathematics Research Notices, 2016 We study ample divisors X with only rational singularities on abelian varieties that decompose into a sum of two lower dimensional subvarieties, X=V+W. For instance, we prove an optimal lower bound on the degree of the corresponding addition map, and show that the minimum can only be achieved if X is a theta divisor.
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Characterization of products of theta divisors [PDF]
Compositio Mathematica, 2014 Abstract We study products of irreducible theta divisors from two points of view. On the one hand, we characterize them as normal subvarieties of abelian varieties such that a desingularization has holomorphic Euler characteristic
Jiang, Zhi +2 more
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Theta Functions on the Theta Divisor
Rocky Mountain Journal of Mathematics, 2010 We show that the gradient and the hessian of the Riemann theta function in dimension n can be combined to give a theta function of order n+1 and modular weight (n+5)/2 defined on the theta divisor. It can be seen that the zero locus of this theta function essentially gives the ramification locus of the Gauss map.
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On the singularities of the theta divisors on Jacobians
, 1997 We study the intersection cohomology of the theta divisors on Jacobians of nonhyperelliptic curves.
Bressler, P., Brylinski, J.-L.
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