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Algebraic Deformations of Polarized Varieties

Published online by Cambridge University Press:  22 January 2016

T. Matsusaka
T. Matsusaka*
Affiliation:
Brandeis University
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Let V be a projectively embeddable complete non-singular variety of dimension n > 1. Let f be a projective embedding of V, U a non-singular variety, W a non-singular variety and φ a morphism of W onto U such that φ-1(u0) = f(V) for some point u0 of U. Denote by ∑(V) the set of all those complete non-singular fibres φ-1(u), u ∈ U, as we consider all possible (f, U, W). Suppose that we call members of ∑(V) (algebraic) deformations of V and propose to study ∑(V) from the stand point of algebraic geometry, as a generalization of the case of curves. This has been taken up at least locally by Kodaira, Spencer, Kuranishi and others in the case of characteristic 0 from a little more general point of view of complex manifolds (cf. [9] and references given in [16]).

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 31 , January 1968 , pp. 185 - 245
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1968

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