A new family of surfaces with ${p}_{g}=0$ and ${K}^{2}=3$

Mendes Lopes, Margarida; Pardini, Rita

doi:10.1016/j.ansens.2004.04.001

A new family of surfaces with

p_{g} = 0

and

K^{2} = 3

Mendes Lopes, Margarida ; Pardini, Rita

Annales scientifiques de l'École Normale Supérieure, Série 4, Tome 37 (2004) no. 4, pp. 507-531.

MR Zbl

DOI : 10.1016/j.ansens.2004.04.001

@article{ASENS_2004_4_37_4_507_0,
     author = {Mendes Lopes, Margarida and Pardini, Rita},
     title = {A new family of surfaces with ${p}_{g}=0$ and ${K}^{2}=3$},
     journal = {Annales scientifiques de l'\'Ecole Normale Sup\'erieure},
     pages = {507--531},
     publisher = {Elsevier},
     volume = {Ser. 4, 37},
     number = {4},
     year = {2004},
     doi = {10.1016/j.ansens.2004.04.001},
     mrnumber = {2097891},
     zbl = {1078.14054},
     language = {en},
     url = {https://www.numdam.org/articles/10.1016/j.ansens.2004.04.001/}
}

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Mendes Lopes, Margarida; Pardini, Rita. A new family of surfaces with ${p}_{g}=0$ and ${K}^{2}=3$. Annales scientifiques de l'École Normale Supérieure, Série 4, Tome 37 (2004) no. 4, pp. 507-531. doi : 10.1016/j.ansens.2004.04.001. https://www.numdam.org/articles/10.1016/j.ansens.2004.04.001/

Bibliographie
Cité par

[1] Barth W., Peters C., Van De Ven A., Compact Complex Surfaces, Ergebnisse der Mathematik und ihrer Grenzgebiete (3), vol. 4, Springer-Verlag, Berlin, 1984. | MR | Zbl

[2] Beauville A., Sur le nombre maximum de points doubles d’une surface dans $P^{3}$ $(μ(5) = 31)$ , in: Journées de Géométrie Algébrique d'Angers, Juillet 1979/Algebraic Geometry, Angers, 1979, Sijthoff & Noordhoff, Alphen aan den Rijn - Germantown, Md., 1980, pp. 207-215. | MR | Zbl

[3] Burniat P., Sur les surfaces de genre $P_{12} > 1$ , Ann. Mat. Pura Appl. (4) 71 (1966). | MR | Zbl

[4] Burns D.M., Wahl J.M., Local contributions to global deformations of surfaces, Invent. Math. 26 (1974) 67-88. | EuDML | MR | Zbl

[5] Catanese F., Singular bidouble covers and the construction of interesting algebraic surfaces, in: Algebraic Geometry: Hirzebruch 70, Contemporary Mathematics, vol. 241, American Mathematical Society, 1999, pp. 97-120. | MR | Zbl

[6] Catanese F., Debarre O., Surfaces with $K^{2} = 2, p_{g} = 1, q = 0$ , J. Reine Angew. Math. 395 (1989) 1-55. | EuDML | MR | Zbl

[7] Cossec F., Projective models of Enriques Surfaces, Math. Ann. 265 (1983) 283-334. | EuDML | MR | Zbl

[8] Cossec F., Dolgachev I., Enriques Surfaces I, Progress in Mathematics, vol. 76, Birkhäuser, 1989. | MR | Zbl

[9] Dolgachev I., Mendes Lopes M., Pardini R., Rational surfaces with many nodes, Compositio Math. 132 (3) (2002) 349-363. | MR | Zbl

[10] Grothendieck A., Fondements de la géométrie algébrique, exposés 232, 236, collected Bourbaki talks, Paris, 1962.

[11] Inoue M., Some new surfaces of general type, Tokyo J. Math. 17 (2) (1994) 295-319. | MR | Zbl

[12] Keum J.H., Some new surfaces of general type with $p_{g} = 0$ , Preprint, 1988.

[13] Van Lint J.H., Introduction to Coding Theory, Graduate Texts in Mathematics, vol. 86, Springer-Verlag, Berlin, 1992. | MR | Zbl

[14] Manetti M., Degeneration of algebraic surfaces and applications to moduli problems, Tesi di Perfezionamento, Scuola Normale Superiore, Pisa, 1996.

[15] Mendes Lopes M., Pardini R., The bicanonical map of surfaces with $p_{g} = 0$ and $K^{2} \geq 7$ , Bull. London Math. Soc. 33 (2001) 265-274. | MR | Zbl

[16] Mendes Lopes M., Pardini R., A connected component of the moduli space of surfaces of general type with $p_{g} = 0$ , Topology 40 (5) (2001) 977-991. | MR | Zbl

[17] Mendes Lopes M., Pardini R., Enriques surfaces with eight nodes, Math. Z. 241 (2002) 673-683. | MR | Zbl

[18] Mendes Lopes M., Pardini R., The bicanonical map of surfaces with $p_{g} = 0$ and $K^{2} \geq 7$ , II, Bull. London Math. Soc. 35 (3) (2003) 337-343. | MR | Zbl

[19] Morrison D., On the moduli of Todorov surfaces, in: Algebraic Geometry and Commutative Algebra, vol. I, Kinokuniya, Tokyo, 1988, pp. 313-355. | MR | Zbl

[20] Mumford D., Geometric Invariant Theory, Ergebnisse der Mathematik und ihrer Grenzgebiete, Neue Folge, vol. 34, Springer-Verlag, Berlin, 1965. | MR | Zbl

[21] Naie D., Surfaces d’Enriques et une construction de surfaces de type général avec $p_{g} = 0$ , Math. Z. 215 (2) (1994) 269-280. | MR | Zbl

[22] Pardini R., The classification of double planes of general type with $K^{2} = 8$ and $p_{g} = 0$ , J. Reine Angew. Math. 417 (1991) 191-213. | Zbl

[23] Pardini R., The classification of double planes of general type with $p_{g} = 0$ and $K^{2} = 8$ , J. Algebra 259 (2003) 95-118. | MR | Zbl

[24] Peters C., On certain examples of surfaces with $p_{g} = 0$ due to Burniat, Nagoya Math. J. 66 (1977) 109-119. | MR | Zbl

[25] Reider I., Vector bundles of rank 2 and linear systems on algebraic surfaces, Ann. of Math. 127 (1988) 309-316. | MR | Zbl

[26] Todorov A.N., A construction of surfaces with $p_{g} = 1$ , $q = 0$ and $2 \leq (K^{2}) \leq 8$ . Counterexamples of the global Torelli theorem, Invent. Math. 63 (2) (1981) 287-304. | MR | Zbl

[27] Xiao G., Finitude de l'application bicanonique des surfaces de type général, Bull. Soc. Math. France 113 (1985) 23-51. | Numdam | MR | Zbl

[28] Xiao G., Degree of the bicanonical map of a surface of general type, Amer. J. Math. 112 (5) (1990) 713-737. | MR | Zbl

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