Boundedness for surfaces in weighted projective 4-spaces
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- by L. V. Rammea and G. K. Sankaran PDF
- Proc. Amer. Math. Soc. 139 (2011), 3393-3403 Request permission
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.
References
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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
- Email: lv.rammea@nul.ls
- G. K. Sankaran
- Affiliation: Department of Mathematical Sciences, University of Bath, Bath BA2 7AY, United Kingdom
- Email: G.K.Sankaran@bath.ac.uk
- 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
- © Copyright 2011
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Proc. Amer. Math. Soc. 139 (2011), 3393-3403
- MSC (2010): Primary 14M07; Secondary 14J25
- DOI: https://doi.org/10.1090/S0002-9939-2011-10774-3
- MathSciNet review: 2813371