Concept
Minimal model program
Related publications (14)
Arithmetic and geometric deformations of threefolds
Stefano Filipazzi, Fabio Bernasconi
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 a ...
Hoboken2023GLOBALLY plus -REGULAR VARIETIES AND THE MINIMAL MODEL PROGRAM FOR THREEFOLDS IN MIXED CHARACTERISTIC
Zsolt Patakfalvi, Joseph Allen Waldron
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 lin ...
SPRINGER HEIDELBERG2023On rationally connected varieties over C1 fields of characteristic 0
We use birational geometry to show that the existence of rational points on proper rationally connected varieties over fields of characteristic 0 is a consequence of the existence of rational points on terminal Fano varieties. We discuss several consequenc ...
MATHEMATICAL SCIENCE PUBL2022Singularities of general fibers and the LMMP
Zsolt Patakfalvi, Joseph Allen Waldron
We use the theory of foliations to study the relative canonical divisor of a normalized inseparable base-change. Our main technical theorem states that it is linearly equivalent to a divisor with positive integer coefficients divisible by p - 1. We deduce ...
JOHNS HOPKINS UNIV PRESS2022Positivity Of The Cm Line Bundle For K-Stable Log Fanos
We prove the bigness of the Chow-Mumford line bundle associated to a Q-Gorenstein family of log Fano varieties of maximal variation with uniformly K-stable general geometric fibers. This result generalizes a theorem of Codogni and Patakfalvi to the logarit ...
2022Vanishing theorems in positive characteristic
The topic of this thesis is vanishing theorems in positive characteristic. In particular, we use "the covering trick of Ekedahl" to investigate the vanishing of for a big and nef Weil divisor on a normal projective variety w ...
EPFL2021Nonperturbative Mellin Amplitudes
Conformal field theory lies at the heart of two central topics in theoretical high energy physics: the study of quantum gravity and the mapping of quantum field theories through the renormalization group. In this thesis we explore a technique to study conf ...
EPFL2021Positivity of the CM line bundle for families of K-stable klt Fano varieties
Zsolt Patakfalvi, Giulio Codogni
The Chow-Mumford (CM) line bundle is a functorial line bundle on the base of any family of klt Fano varieties. It is conjectured that it yields a polarization on the moduli space of K-poly-stable klt Fano varieties. Proving ampleness of the CM line bundle ...
SPRINGER HEIDELBERG2020Birational characterization of abelian varieties and ordinary abelian varieties in characteristic p>0
Let k be an algebraically closed field of characteristic p > 0. We give a birational characterization of ordinary abelian varieties over k: a smooth projective variety X is birational to an ordinary abelian variety if and only if kappa(S)(X) = 0 and b(1)(X ...
DUKE UNIV PRESS2019THE LMMP FOR LOG CANONICAL 3-FOLDS IN CHARACTERISTIC p > 5
We prove that one can run the log minimal model program for log canonical 3-fold pairs in characteristic p > 5. In particular, we prove the cone theorem, contraction theorem, the existence of flips and the existence of log minimal models for pairs with log ...
2018