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\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 for fourfolds.
Arithmetic and geometric deformations of threefolds / Bernasconi, F; Brivio, Ia; Filipazzi, S. - In: BULLETIN OF THE LONDON MATHEMATICAL SOCIETY. - ISSN 0024-6093. - 56:1(2024), pp. 423-443. [10.1112/blms.12942]
Arithmetic and geometric deformations of threefolds
Bernasconi F;
2024
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\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 for fourfolds.| File | Dimensione | Formato | |
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