The fibre of the Prym map in genus four

Hidalgo-Solís, Laura; Recillas-Pishmish, Sevin

Hidalgo-Solís, Laura ; Recillas-Pishmish, Sevin

Bollettino dell'Unione Matematica Italiana, Tome 2-A (1999), p. 219-229 / Harvested from Biblioteca Digitale Italiana di Matematica

Access to full text
Full (PDF)
Full (DjVu)

Résumé

In questa nota si dà una descrizione della fibra della mappa di Prym in genere 4. Se $J X$ è la Jacobiana di una curva di genere 3, allora la fibra della mappa di Prym in $J X$ si ottiene dalla varietà di Kummer $K X$ mediante due scoppiamenti: $σ_{1} : K X (0) \to K X$ che è lo scoppiamento di $K X$ nell'origine e $σ_{2} : \tilde{K X (0)} \to K X (0)$ che è lo scoppiamento lungo una curva isomorfa a $X$ .

Publié le : 1999-02-01

MR 1794551 | Zbl 0945.14016

@article{BUMI_1999_8_2B_1_219_0,
     author = {Laura Hidalgo-Sol\'\i s and Sevin Recillas-Pishmish},
     title = {The fibre of the Prym map in genus four},
     journal = {Bollettino dell'Unione Matematica Italiana},
     volume = {2-A},
     year = {1999},
     pages = {219-229},
     zbl = {0945.14016},
     mrnumber = {1794551},
     language = {en},
     url = {http://dml.mathdoc.fr/item/BUMI_1999_8_2B_1_219_0}
}

Hidalgo-Solís, Laura; Recillas-Pishmish, Sevin. The fibre of the Prym map in genus four. Bollettino dell'Unione Matematica Italiana, Tome 2-A (1999) pp. 219-229. http://gdmltest.u-ga.fr/item/BUMI_1999_8_2B_1_219_0/

Bibliographie

[Be.1] Beauville, A., Prym varietes and the Schottky problem, Invent. Math., 41 (1977), 149-196. | MR 572974 | Zbl 0333.14013

[Be.2] Beauville, A., Variétés de Prym et Jacobiennes intermédiares, Ann. Sci. École Norm. Sup., 10 (1977), 309-391. | MR 472843 | Zbl 0368.14018

[DC-R] Del Centina, A.-Recillas, S., On a property of the Kummer variety and a relation between two moduli spaces of curves, in Algebraic Geometry and Complex Analysis, Proceedings, Lect. Notes in Math., 1414, Springer-Verlag (1989), 28-50. | Zbl 0722.14012

[DM] Deligne, P.-Mumford, D., The irreducibility of the space of curves of a given genus, Publ. Math. I.H.E.S., 36 (1969), 75-109. | MR 262240 | Zbl 0181.48803

[Do.] Donagi, R., The fibers of the Prym map, Cont. Math., Amer. Math. Soc., 136 (1992). | MR 1188194 | Zbl 0783.14025

[DS] Donagi, R.-Smith, R. C., The structure of the Prym map, Acta Math., 146 (1982), 25-102. | MR 594627 | Zbl 0538.14019

[F] Fay, J., Theta Functions on Riemann Surfaces, Lecture Notes, 352, Springer-Verlag (1973). | MR 335789 | Zbl 0281.30013

[FS] Friedman, R.-Smith, R., The generic Torelli theorem for the Prym map, Invent. Math., 74 (1982), 473-490. | MR 664116 | Zbl 0506.14042

[K] Kleiman, S., Algebraic Cycles and the Weil Conjectures, Advanced Studies in Pure Mathematics, North-Holland, 3, Amsterdam (1968). | MR 292838 | Zbl 0198.25902

[Har.] Hartshorne, R., Algebraic Geometry, Springer-Verlag, New York (1977). | MR 463157 | Zbl 0367.14001

[Ma] Masiewicki, L., Universal properties of Prym varieties with an aplication to algebraic curves of genus five, Trans. Amer. Math. Soc, 222 (1976), 221-240. | MR 422289 | Zbl 0333.14012

[M] Mumford, D., Prym Varietes - I, Contributions to Analysis, Academic Press, New York (1974). | MR 379510 | Zbl 0299.14018

[GIT] Mumford, D.-Fogarty, J.-Kirwan, F., Geometric Invariant Theory, third edition, Springer-Verlag, Heidelberg (1994). | MR 1304906 | Zbl 0504.14008

[MP] Muñoz-Porras, J. M., Characterization of the Jacobian varieties in arbitrary characteristic, Comp. Math, 61 (1987), 369-381. | MR 883489 | Zbl 0624.14020

[P] Popp, H., Moduli theory and classification theory of algebraic varieties, Lecture Notes in Math., 620, Spinger-Verlag, Berlin-Heidelberg-New York (1977). | MR 466143 | Zbl 0359.14005

[Rec.1] S., Recillas, Jacobians of curves with $g_{1}^{4}$ 's are Prym's varietes of trigonal curves, Bol. Soc. Mat. Mexicana, 19 (1974), 9-13. | MR 480505 | Zbl 0343.14012

[Rec.2] Recillas, S., Symmetric Cubic Surfaces and Curves of Genus 3 and 4, Boll. Un. Mat. (7), 7-B (1993), 787-819. | MR 1255648 | Zbl 0818.14005

[V] Verra, A., The Fibre of the Prym map in genus three, Math. Ann., 276 (1987), 433-448. | MR 875339 | Zbl 0588.14024

[W] Welters, G., Curves of twice the minimal class on principally polarized abelian variety, Nederl. Akad. Wetensh. Proc. Ser. A., 90 (1987), 87-109. | MR 883371 | Zbl 0644.14014