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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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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