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
     

On birational morphisms between pencils of Del Pezzo surfaces

Author(s): Vitaly Vologodsky
Journal: Proc. Amer. Math. Soc. 129 (2001), 2227-2234.
MSC (2000): Primary 14E05; Secondary 14E30, 14E35
Posted: February 2, 2001
Retrieve article in: PDF
This article is available free of charge

Abstract | References | Similar articles | Additional information

Abstract:

Let $X/S$ and $X'/S'$ be two Del Pezzo fibrations of degrees $d$, $d'$ respectively. Assume that $X$ and $X'$ differ by a flop. Then we prove that $d=d'$ and give a short list of values of other basic numerical invariants of $X$ and $X'$.

References:

[Cor]
A.Corti, Factoring birational maps of threefold after Sarkisov, J. Alg. Geometry, 4 (1993), 223-254. MR 96c:14013

[Ha]
R.Hartshorne, Algebraic Geometry, Springer-Verlag, NewYork-Heidelberg-Berlin, 1977. MR 57:3116

[MM]
S.Mori, S.Mukai, Classification of Fano threefolds with $B_2\ge 2$, Manuscripta Math., 36 (1981), 147-162. MR 83f:14032

[Re]
M.Reid, Birational geometry of 3-folds according to Sarkisov, preprint (1991).

[Sar]
V.G.Sarkisov, Birational maps of standard $\mathbb Q$-Fano fiberings, I.V.Kurchatov Institute Atomic Energy preprint (1989).

Similar Articles:

Retrieve articles in Proceedings of the American Mathematical Society with MSC (2000): 14E05, 14E30, 14E35

Retrieve articles in all Journals with MSC (2000): 14E05, 14E30, 14E35

Additional Information:

Vitaly Vologodsky
Affiliation: Department of Mathematics, University of Georgia, Athens, Georgia 30602
Email: vologods@math.uga.edu

DOI: 10.1090/S0002-9939-01-05905-6
PII: S 0002-9939(01)05905-6
Received by editor(s): May 27, 1998
Received by editor(s) in revised form: December 23, 1999
Posted: February 2, 2001
Communicated by: Ron Donagi
Copyright of article: Copyright 2001, American Mathematical Society

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