Fibrations of low genus, I
Annales scientifiques de l'École Normale Supérieure, Serie 4, Volume 39 (2006) no. 6, pp. 1011-1049.
@article{ASENS_2006_4_39_6_1011_0,
     author = {Catanese, Fabrizio and Pignatelli, Roberto},
     title = {Fibrations of low genus, {I}},
     journal = {Annales scientifiques de l'\'Ecole Normale Sup\'erieure},
     pages = {1011--1049},
     publisher = {Elsevier},
     volume = {Ser. 4, 39},
     number = {6},
     year = {2006},
     doi = {10.1016/j.ansens.2006.10.001},
     mrnumber = {2316980},
     zbl = {1125.14023},
     language = {en},
     url = {http://www.numdam.org/articles/10.1016/j.ansens.2006.10.001/}
}
TY  - JOUR
AU  - Catanese, Fabrizio
AU  - Pignatelli, Roberto
TI  - Fibrations of low genus, I
JO  - Annales scientifiques de l'École Normale Supérieure
PY  - 2006
SP  - 1011
EP  - 1049
VL  - 39
IS  - 6
PB  - Elsevier
UR  - http://www.numdam.org/articles/10.1016/j.ansens.2006.10.001/
DO  - 10.1016/j.ansens.2006.10.001
LA  - en
ID  - ASENS_2006_4_39_6_1011_0
ER  - 
%0 Journal Article
%A Catanese, Fabrizio
%A Pignatelli, Roberto
%T Fibrations of low genus, I
%J Annales scientifiques de l'École Normale Supérieure
%D 2006
%P 1011-1049
%V 39
%N 6
%I Elsevier
%U http://www.numdam.org/articles/10.1016/j.ansens.2006.10.001/
%R 10.1016/j.ansens.2006.10.001
%G en
%F ASENS_2006_4_39_6_1011_0
Catanese, Fabrizio; Pignatelli, Roberto. Fibrations of low genus, I. Annales scientifiques de l'École Normale Supérieure, Serie 4, Volume 39 (2006) no. 6, pp. 1011-1049. doi : 10.1016/j.ansens.2006.10.001. http://www.numdam.org/articles/10.1016/j.ansens.2006.10.001/

[1] Artin M., On isolated rational singularities of surfaces, Amer. J. Math. 88 (1966) 129-136. | MR | Zbl

[2] Atiyah M.F., Vector bundles over an elliptic curve, Proc. Lond. Math. Soc. (3) 7 (1957) 414-452. | MR | Zbl

[3] Barth W., Peters C., Van De Ven A., Compact Complex Surfaces, Ergebnisse der Mathematik und ihrer Grenzgebiete (3), vol. 4, Springer, Berlin, 1984, x+304 pp. | MR | Zbl

[4] Beauville A., L’inégalité p g 2q-4 pour les surfaces de type général, Bull. Soc. Math. France 110 (3) (1982) 344-346. | Numdam | MR | Zbl

[5] Bombieri E., Canonical models of surfaces of general type, Inst. Hautes Études Sci. Publ. Math. 42 (1973) 171-219. | EuDML | Numdam | MR | Zbl

[6] Bombieri, E., Unpublished manuscript, 1972, pp. 1-51.

[7] Catanese F., On a class of surfaces of general type, in: Proc. CIME Conference ‘Algebraic Surfaces', 1977, Liguori Editore, Napoli, 1981, pp. 269-284.

[8] Catanese F., Pluricanonical Gorenstein curves, in: Enumerative Geometry and Classical Algebraic Geometry, Nice, 1981, Progr. Math., vol. 24, Birkhäuser Boston, 1982, pp. 51-95. | MR | Zbl

[9] Catanese F., Singular bidouble covers and the construction of interesting algebraic surfaces, in: Proceedings of the Warsaw Conference in honour of F. Hirzebruch's 70th Birthday, AMS Contemp. Math., vol. 241, 1999, pp. 97-120. | MR | Zbl

[10] Catanese F., Fibred surfaces, varieties isogenous to a product and related moduli spaces, Amer. J. Math. 122 (1) (2000) 1-44. | MR | Zbl

[11] Catanese F., Ciliberto C., Surfaces with p g =q=1, in: Problems in the Theory of Surfaces and Their Classification, Cortona, 1988, Sympos. Math., SSSII, Academic Press, London, 1991, pp. 49-79. | MR | Zbl

[12] Catanese F., Ciliberto C., Symmetric products of elliptic curves and surfaces of general type with p g =q=1, J. Algebraic Geom. 2 (3) (1993) 389-411. | MR | Zbl

[13] Catanese F., Ciliberto C., Mendes Lopes M., On the classification of irregular surfaces of general type with nonbirational bicanonical map, Trans. Amer. Math. Soc. 350 (1) (1998) 275-308. | MR | Zbl

[14] Catanese F., Franciosi M., Divisors of small genus on algebraic surfaces and projective embeddings, in: Proceedings of the Hirzebruch 65 Conference on Algebraic Geometry, Ramat Gan, 1993, Israel Math. Conf. Proc., vol. 9, Bar-Ilan Univ., Ramat Gan, 1996, pp. 109-140. | MR | Zbl

[15] Catanese F., Franciosi M., Hulek K., Reid M., Embedding of curves and surfaces, Nagoya Math. J. 154 (1999) 185-220. | MR | Zbl

[16] Catanese F., Pignatelli R., On simply connected Godeaux surfaces, in: Complex Analysis and Algebraic Geometry, de Gruyter, Berlin, 2000, pp. 117-153. | MR | Zbl

[17] Catanese F., Schreyer F.-O., Canonical projection of irregular algebraic surfaces, in: Algebraic Geometry, de Gruyter, Berlin, 2002, pp. 79-116. | MR | Zbl

[18] Ciliberto C., The bicanonical map for surfaces of general type, in: Algebraic Geometry-Santa Cruz 1995, Proc. Sympos. Pure Math., Part 1, vol. 62, Amer. Math. Soc., Providence, RI, 1997, pp. 57-84. | Zbl

[19] Clemens H., Geometry of formal Kuranishi theory, Adv. Math. 198 (1) (2005) 311-365. | MR | Zbl

[20] Enriques F., Le superficie algebriche, Zanichelli, Bologna, 1949. | MR | Zbl

[21] Esnault H., Viehweg E., Effective bounds for semipositive sheaves and for the height of points on curves over complex function fields, Compositio Math. 76 (1-2) (1990) 69-85. | Numdam | MR | Zbl

[22] Franchetta A., Sul sistema aggiunto ad una curva riducibile, Atti Accad. Naz. Lincei. Rend. Cl. Sci. Fis. Mat. Nat. (8) 6 (1949) 685-687. | MR | Zbl

[23] Franchetta A., Sui sistemi pluricanonici di una superficie algebrica, Univ. Roma. Ist. Naz. Alta Mat. Rend. Mat. e Appl. (5) 8 (1949) 423-440. | MR | Zbl

[24] Franciosi M., Adjoint divisors on algebraic curves, Adv. Math. 186 (2) (2004) 317-333. | MR | Zbl

[25] Fujita T., On Kähler fiber spaces over curves, J. Math. Soc. Japan 30 (4) (1978) 779-794. | MR | Zbl

[26] Fujita T., The sheaf of relative canonical forms of a Kähler fiber space over a curve, Proc. Japan Acad. Ser. A Math. Sci. 54 (7) (1978) 183-184. | MR | Zbl

[27] Hartshorne R., Algebraic Geometry, Graduate Texts in Mathematics, vol. 52, Springer, New York, 1977, xvi+496 pp. | MR | Zbl

[28] Horikawa E., On algebraic surfaces with pencils of curves of genus 2, in: Complex Analysis and Algebraic Geometry, Iwanami Shoten, Tokyo, 1977, pp. 79-90. | MR | Zbl

[29] Horikawa E., Algebraic surfaces of general type with small c 2 1 . V, J. Fac. Sci. Univ. Tokyo Sect. IA Math. 28 (3) (1981) 745-755. | MR | Zbl

[30] Kodaira K., On compact analytic surfaces. II, Ann. of Math. (2) 77 (1963) 563-626, On compact analytic surfaces. III, Ann. of Math. (2) 78 (1963) 1-40. | MR | Zbl

[31] Konno K., Clifford index and the slope of fibered surfaces, J. Algebraic Geom. 8 (2) (1999) 207-220. | MR | Zbl

[32] Konno K., 1-2-3 theorem for curves on algebraic surfaces, J. reine angew. Math. 533 (2001) 171-205. | MR | Zbl

[33] Mendes Lopes, M., The relative canonical algebra for genus three fibrations, PhD thesis, University of Warwick, 1989.

[34] Mumford D., Tata Lectures on Theta I, Progr. in Math., vol. 28, Birkhäuser Boston, 1983, xiii+235 pp. | MR | Zbl

[35] Ogg A.P., On pencils of curves of genus two, Topology 5 (1966) 355-362. | MR | Zbl

[36] Ramanujam C.P., Remarks on the Kodaira vanishing theorem, J. Indian Math. Soc. (N.S.) 36 (1972) 41-51, Supplement, J. Indian Math. Soc. (N.S.) 38 (1, 2, 3, 4) (1974) 121-124, (1975). | MR | Zbl

[37] Reid M., Surfaces with p g =0, K 2 =1, J. Fac. Sci. Univ. Tokyo Sect. IA Math. 25 (1) (1978) 75-92. | MR | Zbl

[38] Reid M., Problems on pencils of small genus, Manuscript, 1990.

[39] Shafarevich I.R., Lectures on minimal models and birational transformations of two dimensional schemes, in: Notes by C.P. Ramanujam, Tata Institute of Fundamental Research Lectures on Mathematics and Physics, vol. 37, Tata Institute of Fundamental Research, Bombay, 1966, iv+175 pp. | MR | Zbl

[40] Xiao G., Surfaces fibrées en courbes de genre deux, in: Lecture Notes in Mathematics, vol. 1137, Springer, Berlin, 1985, x+103 pp. | MR | Zbl

[41] Xiao G., Fibered algebraic surfaces with low slope, Math. Ann. 276 (3) (1987) 449-466. | MR | Zbl

[42] Zucconi F., A note on a theorem of Horikawa, Rev. Mat. Univ. Comput. Madrid 10 (2) (1997) 277-295. | MR | Zbl

Cited by Sources: