Birational rigidity of Fano varieties and field extensions
J\'anos Koll\'ar
TL;DR
This paper investigates how the property of birational rigidity in Fano varieties behaves when extending the base algebraically closed fields, addressing foundational questions in algebraic geometry.
Contribution
It provides new insights into the behavior of birational rigidity under field extensions, clarifying foundational aspects.
Findings
Birational rigidity is preserved under certain field extensions.
New criteria for birational rigidity in extended fields.
Resolution of key foundational questions in the theory.
Abstract
The aim of this note is to settle some foundational questions about the behavior of birational rigidity in extensions of algebraically closed fields.
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Taxonomy
TopicsAlgebraic Geometry and Number Theory · Geometry and complex manifolds · Geometric and Algebraic Topology