Deformations of varieties of general type
J\'anos Koll\'ar
TL;DR
This paper proves that small deformations of projective varieties of general type preserve their general type status and plurigenera, contributing to the understanding of deformation stability in algebraic geometry.
Contribution
It establishes the invariance of general type and plurigenera under small deformations, extending previous results and clarifying deformation properties of algebraic varieties.
Findings
Small deformations preserve the general type property.
Plurigenera remain unchanged under small deformations.
Provides foundational results for deformation theory of algebraic varieties.
Abstract
We prove that small deformations of a projective variety of general type are also projective varieties of general type, with the same plurigenera. Version 2: small changes in first half. Improved version of the second half is now a separate preprint (Seshadri's criterion and openness of projectivity). Version 3: Footnote corrects citation on p.4.
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