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Boundedness for surfaces in weighted projective 4-spaces

Authors: L. V. Rammea and G. K. Sankaran
Journal: Proc. Amer. Math. Soc. 139 (2011), 3393-3403
MSC (2010): Primary 14M07; Secondary 14J25
Published electronically: May 12, 2011
MathSciNet review: 2813371
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Abstract: Ellingsrud and Peskine in 1989 proved that there exists a bound on the degree of smooth nongeneral type surfaces in $ \mathbb{P}^4$. The latest proven bound is 52 by Decker and Schreyer in 2000.

In this paper we consider bounds on the degree of a quasismooth non-general type surface in weighted projective $ 4$-space. We show that such a bound in terms of the weights exists and compute an explicit bound in simple cases.

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Additional Information

L. V. Rammea
Affiliation: Department of Mathematics and Computer Science, The National University of Lesotho, P.O. Roma 180, Lesotho

G. K. Sankaran
Affiliation: Department of Mathematical Sciences, University of Bath, Bath BA2 7AY, United Kingdom

Received by editor(s): November 7, 2009
Published electronically: May 12, 2011
Additional Notes: This work forms part of the Bath Ph.D. thesis of the first author, supported by a Commonwealth Scholarship of the Association of Commonwealth Universities.
Communicated by: Ted Chinburg
Article copyright: © Copyright 2011 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.