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

DOI:
https://doi.org/10.1090/S0002-9947-97-01816-3

MathSciNet review:
1401520

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Abstract | References | Similar Articles | Additional Information

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 . 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:
https://doi.org/10.1090/S0002-9947-97-01816-3

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