On non-projective small resolutions
Serge Lvovski
TL;DR
This paper constructs a broad class of projective threefolds with a single node where their small resolutions are not projective, challenging assumptions about the relationship between projectivity and resolutions.
Contribution
It introduces new examples of threefolds with non-projective small resolutions, expanding understanding of resolution properties in algebraic geometry.
Findings
Existence of projective threefolds with non-projective small resolutions
Construction method for such threefolds
Implications for the theory of algebraic singularities
Abstract
We construct a large class of projective threefolds with one node (aka non-degenerate quadratic singularity) such that their small resolutions are not projective.
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Taxonomy
TopicsFinite Group Theory Research · Advanced Differential Equations and Dynamical Systems · Advanced Topics in Algebra