Projective degenerations of K3 surfaces,Gaussian maps,and Fano threefolds |
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Authors: | Ciro Ciliberto Angelo Lopez Rick Miranda |
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Institution: | (1) Dipartimento di Matematica, Universita di Roma II, Via Fontanile di Carcaricola, 00173 Roma, Italy;(2) Dipartimento di Matematica, Universita di Pavia, Strada Nuova 65, 27100 Pavia, Italy;(3) Department of Mathematics, Colorado State University, 80523 Fort Collins, CO, USA |
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Abstract: | Summary In this article we exhibit certain projective degenerations of smoothK3 surfaces of degree 2g–2 in
g
(whose Picard group is generated by the hyperplane class), to a union of two rational normal scrolls, and also to a union of planes. As a consequence we prove that the general hyperplane section of suchK3 surfaces has a corank one Gaussian map, ifg=11 org13. We also prove that the general such hyperplane section lies on a uniqueK3 surface, up to projectivities. Finally we present a new approach to the classification of prime Fano threefolds of index one, which does not rely on the existence of a line.Oblatum 1-II-1993 & 24-V-1993Research supported in part by NSF grant DMS-9104058 |
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