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Degenerations of K3 surfaces in projective space
Author(s):
Francisco
Javier
Gallego;
B.
P.
Purnaprajna
Journal:
Trans. Amer. Math. Soc.
349
(1997),
2477-2492.
MSC (1991):
Primary 14J10, 14J25, 14J28;
Secondary 14C05, 14C34, 32G20
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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  . 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:
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.
Copyright of article:
Copyright
1997,
American Mathematical Society
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