Available in electronic format
Available in print format		 Transacrions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(e) ISSN 0002-9947(p)
Previous issue | Table of contents | Next issue
Articles in press | Recently posted articles | Most recent issue | All issues
Previous Article | Next Article
     

Surfaces with $p_g=q=3$

Author(s): Christopher D. Hacon; Rita Pardini
Journal: Trans. Amer. Math. Soc. 354 (2002), 2631-2638.
MSC (2000): Primary 14J29
Posted: March 14, 2002
Retrieve article in: PDF DVI PostScript
This article is available free of charge

Abstract | References | Similar articles | Additional information

Abstract: We classify minimal complex surfaces of general type with $p_g=q=3$. More precisely, we show that such a surface is either the symmetric product of a curve of genus $3$ or a free $\mathbb{Z} _2-$quotient of the product of a curve of genus $2$ and a curve of genus $3$. Our main tools are the generic vanishing theorems of Green and Lazarsfeld and the characterization of theta divisors given by Hacon in Corollary 3.4 of Fourier transforms, generic vanishing theorems and polarizations of abelian varieties.

References:

[ACGH]
E. Arbarello, M. Cornalba, P. Griffiths, J. Harris, Geometry of algebraic curves, Volume I, Grundlehren der Math. Wiss. 267, Springer-Verlag, 1985. MR 86h:14019
[Be1]
A. Beauville, Annulation du $H^1$ pour les fibrés en droites plats, Complex Algebraic Varieties, Proc. Conf., Bayreuth, 1990, Springer Lecture Notes in Math. 1507 (1992), 1-15. MR 94a:14048
[Be2]
A. Beauville, L'inegalité $p_g\ge 2q-4$ pour les surfaces de type général, Appendix to [De], Bull. Soc. Math. France 110 (1982), 343-346.
[CCM]
F. Catanese, C. Ciliberto, M. Mendes Lopes, On the classification of irregular surfaces of general type with non birational bicanonical map, Trans. Amer. Math. Soc. 350 (1998), 275-308. MR 98h:14043
[De]
O. Debarre, Inégalités numériques pour les surfaces de type général, Bull. Soc. Math. France 110 (1982), 319-342. MR 84f:14026
[EL]
L. Ein, R. Lazarsfeld, Singularities of theta divisors, and birational geometry of irregular varieties, J. Amer. Math. Soc. 10, 1 (1997), 243-258. MR 97d:14063
[GL1]
M. Green, R. Lazarsfeld, Deformation theory, generic vanishing theorems, and some conjectures of Enriques, Catanese and Beauville, Invent. Math. 90 (1987), 389-407. MR 89b:32025
[GL2]
M. Green, R. Lazarsfeld, Higher obstructions to deforming cohomology groups of line bundles, J. Amer. Math. Soc. 4 (1991), 87-103. MR 92i:32021
[Hac]
C. Hacon, Fourier transforms, generic vanishing theorems and polarizations of abelian varieties, Math. Zeit. 235 (2000), 717-726. MR 2002c:14070
[HP]
C. Hacon, R. Pardini On the birational geometry of varieties of maximal Albanese dimension, J. reine angew. Math. (to appear)

[LB]
H. Lange, C. Birkenhake Complex abelian varieties, Grundlehren der Math. Wiss. 302, Springer-Verlag, 1992. MR 94j:14001

[Pa]
R. Pardini, Abelian covers of algebraic varieties, J. Reine Angew. Math. 417 (1991), 191-213. MR 92g:14012
[Pi]
G. P. Pirola, Surfaces with $p_g=q=3$, Manuscripta Mathematica (to appear)
[Se]
F. Serrano, Isotrivial fibred surfaces, Annali di Matematica Pura ed Applicata (IV), 171 (1996), 63-81. MR 98e:14036

[Si]
C. Simpson, Subspaces of moduli spaces of rank one local systems, Ann. Sci. École Norm. Sup. 4), 26, 3, (1993), 361-401. MR 94f:14008

[Xi]
G. Xiao, Surfaces fibrées en courbes de genre deux, Springer L. N. M. 1137 (1985). MR 88a:14042

Similar Articles:

Retrieve articles in Transactions of the American Mathematical Society with MSC (2000): 14J29

Retrieve articles in all Journals with MSC (2000): 14J29

Additional Information:

Christopher D. Hacon
Affiliation: Department of Mathematics, Surge Bldg., 2nd floor, University of California, Riverside, California 92521-0135
Email: hacon@math.ucr.edu

Rita Pardini
Affiliation: Dipartimento di Matematica, Università di Pisa, Via Buonarroti, 2, 56127 Pisa, Italy
Email: pardini@dm.unipi.it

DOI: 10.1090/S0002-9947-02-02891-X
PII: S 0002-9947(02)02891-X
Received by editor(s): March 5, 2001
Posted: March 14, 2002
Copyright of article: Copyright 2002, American Mathematical Society

  AMS Website Logo Small Comments: webmaster@ams.org
© Copyright 2008, American Mathematical Society
Privacy Statement 		Search the AMSPowered by Google