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Two algebraic deformations of a K3 surface

Published online by Cambridge University Press:  22 January 2016

Daniel Comenetz
Affiliation:
University of Massachusetts at Boston
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Let X be a nonsingular algebraic K3 surface carrying a nonsingular hyperelliptic curve of genus 3 and no rational curves. Our purpose is to study two algebraic deformations of X, viz. one specialization and one generalization. We assume the characteristic ≠ 2. The generalization of X is a nonsingular quartic surface Q in P3 : we wish to show in § 1 that there is an irreducible algebraic family of surfaces over the affine line, in which X is a member and in which Q is a general member. The specialization of X is a surface Y having a birational model which is a ramified double cover of a quadric cone in P3 .

Type
Research Article
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1981

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