Smoothings of Fano schemes with normal crossing singularities of dimension at most three

2009/07/21 by Nikolaos Tziolas, Tziolas, Nikolaos
Mathematics · Physics and Astronomy · #14D06 #14D15 #14J45 #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Algebraic structures and combinatorial models #FOS: Mathematics #Nonlinear Waves and Solitons #math.AG #msc:14D06 #msc:14D15 #msc:14J45

paper · pdf · doi:10.48550/arxiv.0907.3641

22 pages

arxiv created 2009/07/21 · openalex publication_date 2009/07/21 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study the deformation theory of a Fano variety X with normal crossing singularities of dimension at most three. We obtain a formula for the sheaf T¹(X) of first order deformations of X in a suitable log resolution of X and its singular locus Z and we obtain explicit criteria for the existence of smoothings of X.

Related

• Smoothings of Fano varieties with normal crossing singularities
• First order deformations of schemes with normal crossing singularities
• Projective smoothing of varieties with simple normal crossings
• Deformations of weak Fano 3-folds with only terminal singularities
• Deformations of singular Fano and Calabi-Yau varieties