Mediaspace scheduled maintenance: Aug 25, 2026 07:00 - 12:00 AM. During this time, videos will be temporarily unavailable. Check status updates.

Publication

GLOBALLY plus -REGULAR VARIETIES AND THE MINIMAL MODEL PROGRAM FOR THREEFOLDS IN MIXED CHARACTERISTIC

Zsolt Patakfalvi
2023
Journal Articles

Abstract

We establish the Minimal Model Program for arithmetic threefolds whose residue characteristics are greater than five. In doing this, we generalize the theory of global F-regularity to mixed characteristic and identify certain stable sections of adjoint line bundles. Finally, by passing to graded rings, we generalize a special case of Fujita's conjecture to mixed characteristic.

Official source

Zsolt Patakfalvi
2023
Journal Articles

Abstract

Official source

Related concepts (32)

Graded ring

In mathematics, in particular abstract algebra, a graded ring is a ring such that the underlying additive group is a direct sum of abelian groups such that . The index set is usually the set of nonnegative integers or the set of integers, but can be any monoid. The direct sum decomposition is usually referred to as gradation or grading. A graded module is defined similarly (see below for the precise definition). It generalizes graded vector spaces. A graded module that is also a graded ring is called a graded algebra.

Morphism of algebraic varieties

In algebraic geometry, a morphism between algebraic varieties is a function between the varieties that is given locally by polynomials. It is also called a regular map. A morphism from an algebraic variety to the affine line is also called a regular function. A regular map whose inverse is also regular is called biregular, and the biregular maps are the isomorphisms of algebraic varieties.

Graded-commutative ring

In algebra, a graded-commutative ring (also called a skew-commutative ring) is a graded ring that is commutative in the graded sense; that is, homogeneous elements x, y satisfy where |x | and |y | denote the degrees of x and y. A commutative (non-graded) ring, with trivial grading, is a basic example. An exterior algebra is an example of a graded-commutative ring that is not commutative in the non-graded sense. A cup product on cohomology satisfies the skew-commutative relation; hence, a cohomology ring is graded-commutative.

Related publications (37)

GLOBALLY plus -REGULAR VARIETIES AND THE MINIMAL MODEL PROGRAM FOR THREEFOLDS IN MIXED CHARACTERISTIC

Graph Chatbot

Multigraded algebras and multigraded linear series

Excited State-Specific CASSCF Theory for the Torsion of Ethylene

Global Regularity For The Nonlinear Wave Equation With Slightly Supercritical Power