Variétés de Prym, conjecture de la trisécante et ensembles d'Andreotti et Mayer

Debarre, Olivier

Membres du jury : Raynaud, Michel ; Arbarello, Enrico ; Beauville, Arnaud ; Herman, Michel ; Welters, Gerald

Thèses d'Orsay, no. 204 (1987) , 252 p.

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@phdthesis{BJHTUP11_1987__0204__A1_0,
     author = {Debarre, Olivier},
     title = {Vari\'et\'es de {Prym,} conjecture de la tris\'ecante et ensembles {d'Andreotti} et {Mayer}},
     series = {Th\`eses d'Orsay},
     publisher = {Universit\'e de Paris-Sud Centre d'Orsay},
     number = {204},
     year = {1987},
     language = {fr},
     url = {http://www.numdam.org/item/BJHTUP11_1987__0204__A1_0/}
}

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%I Université de Paris-Sud Centre d'Orsay
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Debarre, Olivier. Variétés de Prym, conjecture de la trisécante et ensembles d'Andreotti et Mayer. Thèses d'Orsay, no. 204 (1987), 252 p. http://numdam.org/item/BJHTUP11_1987__0204__A1_0/

Bibliographie
Cité par

[An-M] A. Andreotti, A. Mayer.- On period relations for abelian integrals on algebraic curves. Ann. Sc. Norm. Sup. Pisa 21 (1967), 189-238. | MR | Zbl | Numdam

[Ar] E. Arbarello.- Fay's Trisecant Formula and a Characterization of Jacobian Varieties. A paraître. | Zbl | DOI

[A-C-G-H 1] E. Arbarello, M. Cornalba, P.A. Griffiths, J. Harris.- Geometry of Algebraic Curves, I. Springer Verlag, New York. | Zbl | DOI

[A-C-G-H 2] E. Arbarello, M. Cornalba, P.A. Griffiths, J. Harris.- Geometry of Algebraic Curves, II. A paraître. | MR

[Ar-D 1] E. Arbarello, C. De Concini.- On a set of equations characterizing Riemann matrices. Ann. of Math. 120, 119-140 (1984). | MR | Zbl | DOI

[Ar-D 2] E. Arbarello, C. De Concini.- Another proof of a conjecture of S.P. Novikov on periods of Abelian integrals on Riemann surfaces. A paraître. | Zbl

[Ba] W. Barth.- Fortsetzung meromorpher Funktionen in Tori und Komplexprojektiven Räumen. Invent. Math. 5 (1968), 42-62. | MR | Zbl | DOI

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

[Be 2] A. Beauville.- Variétés de Prym et jacobiennes intermédiaires. Ann. Sci. Ecole Norm. Sup. 10 (1977), 309-391. | MR | Zbl | Numdam | DOI

[Be 3] A. Beauville.- Sous-variétés spéciales des variétés de Prym. Comp. Math. 45 (1982), 357-383. | MR | Zbl | Numdam

[Be-D 1] A. Beauville, O. Debarre.- Une relation entre deux approches du problème de Schottky. Invent. Math. 86 (1986), 195-207. | MR | Zbl | DOI

[Be-D 2] A. Beauville, O. Debarre.- Sur le problème de Schottky pour les variétés de Prym. A paraître. | Zbl | Numdam

[Ci] C. Ciliberto.- On a proof of Torelli's Theorem. Ravello. Springer Lecture Notes 997 (1983), 113-123. | MR | Zbl

[Cl-G] H. Clemens, P. Griffiths.- The intermediate Jacobian of the cubic threefold. Ann. of Math. 95 (1972), 281-356. | MR | Zbl | DOI

[D 1] O. Debarre.- Sur la démonstration de A. Weil du théorème de Torelli pour les courbes. Comp. Math. 58 (1986), 3-11. | MR | Zbl | Numdam

[D 2] O. Debarre.- Sur les variétés abéliennes dont le diviseur thêta est singulier en codimension 3. A paraître. | Zbl | DOI

[D 3] O. Debarre.- Variétés de Prym et ensembles d'Andreotti-Mayer. A paraître. | Zbl | DOI

[De] P. Deligne.- Le lemme de Gabber. In séminaire sur les pinceaux arithmétiques : la conjecture de Mordell. Exposé V, Astérisque 127 (1985). | MR | Zbl | Numdam

[De-M] P. Deligne, D. Mumford.- The irreducibility of the space of curves of given genus. Publ. Math. IHES, Paris, 36 (1969), 75-109. | MR | Zbl | Numdam | DOI

[Do] R. Donagi.- The tetragonal construction. Bull. Amer. Math. Soc. 4 (1981), 181-185. | MR | Zbl | DOI

[Do-S] R. Donagi, R.C. Smith.- The structure of the Prym map. Acta Math. 146 (1981), 25-102. | MR | Zbl | DOI

[Du] B.A. Dubrovin.- Theta functions and non-linear equations. Russian Math. Surveys 36, n° 2 (1981), 11-92. | Zbl | MR | DOI

[Fr-S 1] R. Friedman, R. Smith.- The generic Torelli theorem for the Prym map. Invent. Math. 67 (1982), 473-490. | MR | Zbl | DOI

[Fr-S 2] R. Friedman, R. Smith.- Degenerations of Prym Varieties and Intersections of Three Quadrics. Invent. Math. 85 (1986), 615-635. | MR | Zbl | DOI

[Fu-L] W. Fulton, R. Lazarsfeld.- On the connectedness of degeneracy loci and special divisors. Acta Math. 146 (1981), 271-283. | MR | Zbl | DOI

[Gi] D. Gieseker.- Stable Curves and Special Divisors : Petri's Conjecture. Invent. Math. 66 (1982), 251-275. | MR | Zbl | DOI

[Gr 1] M. Green.- Quadrics of rank four in the ideal of a canonical curve. Invent. Math. 75 (1984), 85-104. | MR | Zbl | DOI

[Gr 2] M. Green.- Koszul cohomology and the geometry of projective varieties. J. Diff. Geom. 19 (1984), 125-171. | MR | Zbl

[Gr-L] M. Green, R. Lazarsfeld.- On the projective normality of complete linear series on an algebraic curve. Invent. Math. 83 (1986), 73-90. | MR | Zbl | DOI

[Gri-H] P. Griffiths, J. Harris.- Principles of Algebraic Geometry. Wiley-Interscience New-York (1978). | MR | Zbl

[Gro 1] A. Grothendieck.- Eléments de Géométrie Algébrique. Publ. IHES. | Numdam | Zbl

[Gro 2] A. Grothendieck.- Techniques de construction en Géométrie Analytique IX. Quelques problèmes de modules. Séminaire H. Cartan, 13e année, Exposé n° 16 (1960/61).

[Gro 3] A. Grothendieck.- Cohomologie locale des faisceaux cohérents et théorèmes de Lefschetz locaux et globaux (SGA 2). Masson et North-Holland, Paris-Amsterdam (1968). | MR | Zbl

[H] J. Harris.- Theta-characteristics on algebraic curves. Trans. Amer. Math. Soc. 271 (1982), 611-638. | MR | Zbl | DOI

[H-M] J. Harris, D. Mumford.- On the Kodaira Dimension of the Moduli Space of Curves. Invent. Math. 67 (1982), 23-86. | MR | Zbl | DOI

[Ha] R. Hartshorne.- Algebraic Geometry. Springer-Verlag, New York-Heidelberg-Berlin (1977). | MR | Zbl | DOI

[Ig 1] J.I. Igusa.- A desingularization problem in the theory of Siegel modular functions. Math. Ann. 168 (1967), 228-260. | MR | Zbl | DOI

[Ig 2] J.I. Igusa.- Theta functions. Grundlehren der Math. Wiss., 194 Springer-Verlag (1972). | MR | Zbl

[Ig 3] J.I. Igusa.- On the irreducibility of Schottky's divisor. J. Fac. Sci. Tokyo 28 (1981), 531-545. | MR | Zbl

[Ke-L] G. Kempf, D. Laksov.- The determinantal formula of Schubert calculus. Acta Math. 132 (1974), 153-162. | MR | Zbl | DOI

[Kl-L] S. Kleiman, D. Laksov.- Another proof of the existence of special divisors. Acta Math. 132 (1974), 163-176. | MR | Zbl | DOI

[M] I.G. Macdonald.- Symmetric products of an algebraic curve. Topology 1 (1962), 319-343. | MR | Zbl | DOI

[Ma] H.H. Martens.- On the variety of special divisors on a curve. J. Reine Angew. Math. 227 (1967), 111-120. | MR | Zbl

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

[Mu 1] D. Mumford.- On the Kodaira Dimension of the Siegel Modular Variety. Springer Lecture Notes 997, Springer-Verlag, New York (1983), 348-375. | MR | Zbl

[Mu 2] D. Mumford.- Prym Varieties I. Contributions to Analysis. Acad. Press, New York (1974), 325-350. | MR | Zbl

[Mu 3] D. Mumford.- Theta characteristics of an algebraic curve. Ann. Sci. Ecole Norm. Sup. 4 (1971), 181-192. | MR | Zbl | Numdam | DOI

[Mu 4] D. Mumford.- Varieties defined by Quadratic Equations. C.I.M.E., Varenna, 1969. | MR | Zbl

[Mu 5] D. Mumford.- On the equations defining abelian varieties I. Invent. Math. 1 (1966), 287-354. | MR | Zbl | DOI

[Mu 6] D. Mumford.- Abelian Varieties. Tata Studies in Math. 5, Oxford (1970). | MR | Zbl

[Mu 7] D. Mumford.- Analytic construction of degenerating abelian varieties. Comp. Math. 24 (1972), 239-272. | MR | Zbl | Numdam

[Mu 8] D. Mumford.- Curves and their Jacobians. Ann Arbor, The University of Michigan Press (1978). | MR | Zbl

[Mu 9] D. Mumford.- Varieties defined by quadratic equations (with an appendix by G. Kempf). Questions on algebraic varieties, 29-100, ed. Cremonese, Roma (1970). | MR | Zbl

[Mu 10] D. Mumford.- Tata lectures on Theta II. Progress in Math. 43, Birkhäuser, Boston-Bâle-Stuttgart (1984). | MR | Zbl

[Na] Y. Namikawa.- A new compactification of the Siegel space and degeneration of abelian varieties. Math. Ann. 221 (1976), 97-142 et 201-242. | MR | Zbl | DOI

[Ra] Z. Ran.- On subvarieties of abelian varieties. Invent. Math. 62 (1981), 459-479. | MR | Zbl | DOI

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

[SD] B. Saint-Donat.- On Petri's analysis of the linear system of quadrics through a canonical curve. Math. Ann. 206 (1973), 157-175. | MR | Zbl | DOI

[Sh] T. Shiota.- Characterization of Jacobian varieties in terms of soliton equations. Invent. Math. 83 (1986), 333-382. | MR | Zbl | DOI

[Sho 1] V.V. Shokurov.- Prym varieties : Theory and Applications. Math. USSR Izvestja, 23 (1984), N° 1. | MR | Zbl

[Sho 2] V.V. Shokurov.- Distinguishing Prymians from Jacobians. Invent. Math. 65 (1981), 209-219. | MR | Zbl | DOI

[Sm-V] R. Smith, R. Varley.- Components of the locus of singular theta divisors of genus five. In Algebraic Geometry Sitges 1983. Springer Lecture Notes 1124, Springer-Verlag (1983), 338-416. | MR | Zbl

[Te] M. Teixidor.- For which Jacobi varieties is $Sing θ$ reducible ? J. Reine Angew. Math. 354 (1984), 141-149. | MR | Zbl

[Tj 1] A.N. Tjurin.- Five Lectures on three-dimensional varieties. Russian Math. Surveys 27 (1972), 1-53. | Zbl | MR | DOI

[Tj 2] A.N. Tjurin.- On the Intersections of Quadrics. Russian Math. Surveys 30 (1975). | Zbl | MR

[Tj 3] A.N. Tjurin.- The Geometry of the Poincaré Theta-Divisor of a Prym Variety. Math. USSR Izvestja 9 (1975), 951-986. | Zbl | MR | DOI

[V] B. Van Geemen.- The Schottky Problem and Moduli Spaces of Kummer Varieties. Thesis, University of Utrecht (1985).

[Va] R. Varley.- Weddle's surfaces, Humbert's curves, and a certain $4$ -dimensional abelian variety. Am. J. of Math. 108 (1986), 931-952. | MR | Zbl | DOI

[W] A. Weil.- Zum Beweis des Torellischen Satzes. Nachr. Akad. Wiss. Göttingen Math. Phys. Kl. 2 (1957), 33-53. | MR | Zbl

[We 1] G. Welters.- A theorem of Gieseker-Petri type for Prym varieties. Ann. Sci. Ecole Norm. Sup. 18 (1985), 671-683. | MR | Zbl | Numdam | DOI

[We 2] G. Welters.- The surface $C - C$ on Jacobi varieties and 2nd order theta functions. Acta Math. 157 (1986), 1-22. | MR | Zbl | DOI

[We 3] G. Welters.- Abel-Jacobi isogenies for certain types of Fano threefolds. Mathematisch Centrum, Amsterdam (1981). | MR | Zbl

[We 4] G. Welters.- Recovering the curve data from a general Prym variety. Amer. J. of Math. A paraître. | MR | Zbl

[We 5] G. Welters.- Polarized abelian varieties and the heat equation. Comp. Math. 49 (1983), 173-194. | MR | Zbl | Numdam

[We 6] G. Welters.- A characterization of non-hyperelliptic Jacobi varieties. Invent. Math. 74 (1983), 437-440. | MR | Zbl | DOI

[We 7] G. Welters.- A criterion for Jacobi varieties. Ann. of Math. 120 (1984), 497-504. | MR | Zbl | DOI

[We 8] G. Welters.- On flexes of the Kummer variety. Proc. Kon. Ned. Akad. van Wetenschappen, Series A, 86 ; Indagationes Math. 45 (1983), 501-520. | MR | Zbl | DOI

[Z] O. Zariski.- On a theorem of Severi. Amer. J. of Math. 50 (1928), 87-92. | MR | JFM | DOI