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Publication

Arithmetic and geometric deformations of threefolds

Stefano Filipazzi, Fabio Bernasconi
2023
Journal Articles

Résumé

We show that mixed-characteristic and equicharacteristic 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 for fourfolds.

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https://infoscience.epfl.ch/entities/publication/2c6007a6-632b-4313-8297-df5d354a497b

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Stefano Filipazzi, Fabio Bernasconi
2023
Journal Articles

Résumé

Source officielle

https://infoscience.epfl.ch/entities/publication/2c6007a6-632b-4313-8297-df5d354a497b

À propos de ce résultat

Concepts associés (32)

Canonical bundle

In mathematics, the canonical bundle of a non-singular algebraic variety of dimension over a field is the line bundle , which is the nth exterior power of the cotangent bundle on . Over the complex numbers, it is the determinant bundle of the holomorphic cotangent bundle . Equivalently, it is the line bundle of holomorphic n-forms on . This is the dualising object for Serre duality on . It may equally well be considered as an invertible sheaf.

Minimal model program

In algebraic geometry, the minimal model program is part of the birational classification of algebraic varieties. Its goal is to construct a birational model of any complex projective variety which is as simple as possible. The subject has its origins in the classical birational geometry of surfaces studied by the Italian school, and is currently an active research area within algebraic geometry. The basic idea of the theory is to simplify the birational classification of varieties by finding, in each birational equivalence class, a variety which is "as simple as possible".

Kodaira dimension

In algebraic geometry, the Kodaira dimension κ(X) measures the size of the canonical model of a projective variety X. Igor Shafarevich in a seminar introduced an important numerical invariant of surfaces with the notation κ. Shigeru Iitaka extended it and defined the Kodaira dimension for higher dimensional varieties (under the name of canonical dimension), and later named it after Kunihiko Kodaira. The canonical bundle of a smooth algebraic variety X of dimension n over a field is the line bundle of n-forms, which is the nth exterior power of the cotangent bundle of X.

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Publications associées (28)

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Arithmetic and geometric deformations of threefolds

Graph Chatbot

Rational points on 3-folds with nef anti-canonical class over finite fields

Experimental observation of topological transition in linear and nonlinear parametric oscillators

The Nonvanishing Problem for varieties with nef anticanonical bundle