Available in electronic format
Available in print format		 Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826 (e) ISSN 0002-9939 (p)
Previous issue | Table of contents | Next issue
Articles in press | Recently posted articles | Most recent issue | All issues
Previous Article | Next Article
     

Stable degenerations of surfaces isogenous to a product of curves

Author(s): Michael van Opstall
Journal: Proc. Amer. Math. Soc. 134 (2006), 2801-2806.
MSC (2000): Primary 14J10
Posted: April 11, 2006
Retrieve article in: PDF

Abstract | References | Similar articles | Additional information

Abstract: We show that an example of Catanese yields nonrigid surfaces that are diffeomorphic, yet lie on different connected components of the moduli space of stable surfaces.

References:

[AAL81]
W. A. Adkins, A. Andreotti, and J. V. Leahy.
Weakly normal complex spaces, volume 55 of Contributi del Centro Linceo Interdisciplinare di Scienze Matematiche e loro Applicazioni.
Accademia Nazionale dei Lincei, Rome, 1981. MR 0695003 (84g:32013)

[Ale94]
V. Alexeev.
Boundedness and $ K^2$ for log surfaces.
Internat. J. Math., 5(6):779-810, 1994. MR 1298994 (95k:14048)

[BC04]
I. Bauer and F. Catanese.
Some new surfaces with $ p_g=q=0$.
The Fano Conference, 123-142.
Univ. Torino, Turin. 2004. MR 2112572 (2005k:14079)

[Cat00]
F. Catanese.
Fibred surfaces, varieties isogenous to a product and related moduli spaces.
Amer. J. Math., 122(1):1-44, 2000. MR 1737256 (2001i:14048)

[Cat03]
F. Catanese.
Moduli spaces of surfaces and real structures.
Ann. of Math., 158:539-554, 2003. MR 2018929 (2005d:14053)

[HM98]
J. Harris and I. Morrison.
Moduli of curves, volume 187 of Graduate Texts in Mathematics.
Springer-Verlag, New York, 1998. MR 1631825 (99g:14031)

[KK02]
V. Kulikov and V. Kharlamov.
On real structures on rigid surfaces.
Izv. Math., 66(1):133-150, 2002. MR 1917540 (2003h:14089)

[KM98]
J. Kollár and S. Mori.
Birational geometry of algebraic varieties, volume 134 of Cambridge Tracts in Mathematics.
Cambridge University Press, Cambridge, 1998. MR 1658959 (2000b:14018)

[Kol90]
J. Kollár.
Projectivity of complete moduli.
J. Differential Geom., 32(1):235-268, 1990. MR 1064874 (92e:14008)

[KSB88]
J. Kollár and N. I. Shepherd-Barron.
Threefolds and deformations of surface singularities.
Invent. Math., 91(2):299-338, 1988. MR 0922803 (88m:14022)

[Man01]
M. Manetti.
On the moduli space of diffeomorphic algebraic surfaces.
Invent. Math., 143(1):29-76, 2001. MR 1802792 (2001j:14050)

[Tuf93]
S. Tufféry.
Déformations de courbes avec action de groupe.
Forum Math., 5(3):243-259, 1993. MR 1216034 (94d:14012)

[vO05]
M. A. van Opstall.
Moduli of products of curves.
Arch. Math. (Basel), 84(2):148-154, 2005. MR 2120708

Similar Articles:

Retrieve articles in Proceedings of the American Mathematical Society with MSC (2000): 14J10

Retrieve articles in all Journals with MSC (2000): 14J10

Additional Information:

Michael van Opstall
Affiliation: Departmant of Mathematics, University of Utah, 155 South 1400 East, Room 233, Salt Lake City, Utah 84112-0090
Email: opstall@math.utah.edu

DOI: 10.1090/S0002-9939-06-08517-0
PII: S 0002-9939(06)08517-0
Received by editor(s): December 16, 2004
Received by editor(s) in revised form: April 18, 2005
Posted: April 11, 2006
Communicated by: Michael Stillman
Copyright of article: Copyright 2006, American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.

  AMS Website Logo Small Comments: webmaster@ams.org
© Copyright 2009, American Mathematical Society
Privacy Statement 		Search the AMSPowered by Google