Deformations of Q-Calabi-Yau 3-folds and Q-Fano 3-folds of Fano index 1
Tatsuhiro Minagawa
TL;DR
This paper proves that certain classes of three-dimensional algebraic varieties with mild singularities, specifically Q-Calabi-Yau and Q-Fano 3-folds with Fano index 1, admit smoothings that resolve their singularities.
Contribution
It establishes the existence of Q-smoothings for Q-Calabi-Yau 3-folds and Q-Fano 3-folds of Fano index 1 with terminal singularities, advancing deformation theory in algebraic geometry.
Findings
Q-Calabi-Yau 3-folds with terminal singularities have Q-smoothings
Q-Fano 3-folds of Fano index 1 with terminal singularities have Q-smoothings
The results extend deformation theory for these classes of threefolds.
Abstract
In this article, we prove that any Q-Calabi-Yau 3-fold with only ordinary terminal singularities and any Q-Fano 3-fold of Fano index 1 with only terminal singularities have Q-smoothings.
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Taxonomy
TopicsAlgebraic Geometry and Number Theory · Geometry and complex manifolds · Advanced Algebra and Geometry