Book Chapter10.1007/BFB0093588
Les singularites du diviseur Θ de la jacobienne intermediaire de l’hypersurface cubique dans IP4
Arnaud Beauville
- 01 Jan 1982
- pp 190-208
86
TL;DR: In this article, Mumford pointed out that la cubique n'est pas rationnelle (un partie des r~sultats de [C-G] avait 6t6 obtenue independenue indienue independence par Tjurin IT2]).
read more
Abstract: Introduction La g6om~trie de l'hypersurface cubique de dimension 3 a ~t6 61ucid6e par Clemens et Griffiths ~C-G] ~ citons, parmi les r~sultats les plus frappants, le th~oreme de Torelli et le fait que la cubique n'est pas rationnelle (une partie des r~sultats de [C-G] avait 6t6 obtenue ind6pendamment par Tjurin IT2]). Clemens et Griffiths utilisaient des arguments d61icats de d~g~n~reseence ~ Mumford a observ~ qu'on peut d6duire l'irrationalit~ de la cubique de la th~orie des vari~t~s de Prym.
read more
Chat with Paper
AI Agents for this Paper
Find similar papers on Google Scholar, PubMed and Arxiv
Write a critical review of this paper
Analyze citations of this paper to find unaddressed research gaps
Citations
Orbifold Aspects of Certain Occult Period Maps
TL;DR: In this paper, the automorphism groups of Hodge structures of cubic threefolds and cubic fourfolds were characterized and the action of these automorphisms on Hodge structure of associated cyclic covers was confirmed.
10
Orbifold Aspects of Certain Occult Period Maps
TL;DR: In this article, the automorphism groups of Hodge structures of cubic threefolds and cubic fourfolds were characterized and the action of their automorphisms on Hodge structure of associated cyclic covers was confirmed.
9
•Posted Content
A Prym construction for the cohomology of a cubic hypersurface
TL;DR: In this article, a natural isomorphism between the intermediate jacobian of a conic-bundle and the Prym variety of a naturally defined ''etale double cover of the discrminant curve of the conicbundle was given.
7
Arithmetic Torelli maps for cubic surfaces and threefolds
TL;DR: In this paper, the moduli space of cubic surfaces with an open substack of a certain modulus space of abelian varieties has been identified, and a construction which works for cubics over an arithmetic base has been given.
•Posted Content
Theta-duality on Prym varieties and a Torelli Theorem
Martí Lahoz,Juan Carlos Naranjo +1 more
TL;DR: In this article, the authors prove the schematic theta-dual equalities in the Prym variety T(C') = V^2 and T(V^2) = C', where V is the Brill-Noether locus of P associated to p considered by Welters.
7
References
The intermediate Jacobian of the cubic threefold
TL;DR: JSTOR is a not-for-profit service that helps scholars, researchers, and students discover, use, and build upon a wide range of content in a trusted digital archive.
Variétés de Prym et jacobiennes intermédiaires
TL;DR: The article as discussed by the authors implique l'accord avec les conditions générales d'utilisation ( http://www.dma.org/ legal.php).
Prym Varieties I
David Mumford
- 01 Jan 1974
TL;DR: In this article, the first steps in a purely algebraic version (in all characteristics except two) of the Riemann-Prym-Wirtinger-Schottky-Jung theory of double coverings of one curve over another were presented.
326
Five Lectures on Three-Dimensional Varieties
TL;DR: In the course of five lectures delivered in the seminar on algebraic geometry at the Moscow State University as discussed by the authors, the main object was to make extensive use of the Abel-Jacobi mapping for families of curves on three-dimensional varieties.
114