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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Degenerations of K3 surfaces in projective space


Authors: Francisco Javier Gallego and B. P. Purnaprajna
Journal: Trans. Amer. Math. Soc. 349 (1997), 2477-2492
MSC (1991): Primary 14J10, 14J25, 14J28; Secondary 14C05, 14C34, 32G20
MathSciNet review: 1401520
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Abstract: The purpose of this article is to study a certain kind of numerical K3 surfaces, the so-called K3 carpets. These are double structures on rational normal scrolls with trivial dualizing sheaf and irregularity $0$. As is deduced from our study, K3 carpets can be obtained as degenerations of smooth K3 surfaces. We also study the Hilbert scheme near the locus parametrizing K3 carpets, characterizing those K3 carpets whose corresponding Hilbert point is smooth. Contrary to the case of canonical ribbons, not all K3 carpets are smooth points of the Hilbert scheme.


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Additional Information

Francisco Javier Gallego
Affiliation: Departamento de Álgebra, Facultad de Matemáticas, Universidad Complutense de Madrid, 28040 Madrid, Spain
Email: gallego@eucmos.sim.ucm.es

B. P. Purnaprajna
Affiliation: Department of Mathematics, Brandeis University, Waltham, Massachusetts 02254-9110
Address at time of publication: Department of Mathematics, Oklahoma State University, Stillwater, Oklahoma 74078
Email: purna@littlewood.math.okstate.edu

DOI: http://dx.doi.org/10.1090/S0002-9947-97-01816-3
PII: S 0002-9947(97)01816-3
Received by editor(s): January 11, 1996
Additional Notes: We are very pleased to thank our advisor David Eisenbud for his help, patience and encouragement. We would also like to thank Andrea Bruno and Enrique Arrondo for helpful discussions and Mohan Kumar for his helpful comments and suggestions.
Article copyright: © Copyright 1997 American Mathematical Society