2025/06/11 by Robert Friedman, Friedman, Robert · 1 citation
Mathematics · #14J32 (Primary) 14D15 #32G05 (Secondary) #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Commutative Algebra and Its Applications #FOS: Mathematics #Geometry and complex manifolds
paper · pdf · doi:10.48550/arxiv.2506.09857
openalex publication_date 2025/06/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Let Y be a compact Gorenstein analytic space with only isolated singularities and trivial dualizing sheaf. A recent paper of Imagi studies the deformation theory of Y in case the singularities of Y are weighted homogeneous and rational and Y is Kähler. In this note, assuming that H1(Y;OY) =0, we generalize Imagi's results to the case where the singularities of Y are Du Bois, with no assumption that they be weighted homogeneous, and where the Kähler assumption is replaced by the hypothesis that there is a resolution of singularities of Y satisfying the ∂∂-lemma. As a consequence, if the singularities of Y are additionally local complete intersections, then the deformations of Y are unobstructed. The log Calabi-Yau and Fano cases are also discussed.