Arithmetic and geometric deformations of 3-folds

Abstract

We show that mixed-characteristic and equi-characteristic small deformations of 3-dimensional canonical (resp. terminal) singularities with perfect residue field of characteristic $p>5$ are canonical (resp. terminal). We discuss applications to arithmetic and geometric families of 3-dimensional Fano varieties and minimal models with canonical singularities. Our results are contingent upon the existence of log resolutions of 4-folds.

arXiv commentv3: 19 pages, minor corrections. To appear in Bull. London Math. Soc

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