Publication
On the projectivity of some moduli spaces of varieties
Related publications (34)
MODULI OF Q-GORENSTEIN PAIRS AND APPLICATIONS
We develop a framework to construct moduli spaces of Q-Gorenstein pairs. To do so, we fix certain invariants; these choices are encoded in the notion of Q-stable pair. We show that these choices give a proper moduli space with projective coarse moduli spac ...
Providence2024BPS invariants from p-adic integrals
Dimitri Stelio Wyss, Francesca Carocci, Giulio Orecchia
We define p-adic BPS or pBPS invariants for moduli spaces M-beta,M-chi of one-dimensional sheaves on del Pezzo and K3 surfaces by means of integration over a non-archimedean local field F. Our definition relies on a canonical measure mu can on the F-analyt ...
Cambridge Univ Press2024GLOBALLY 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 HEIDELBERG2023NORM TORI OF ETALE ALGEBRAS AND UNRAMIFIED BRAUER GROUPS
Eva Bayer Fluckiger, Ting-Yu Lee
Let k be a field, and let L be an etale k-algebra of finite rank. If a is an element of k(x), let X-a be the affine variety defined by N-L/k(x) = a. Assuming that L has at least one factor that is a cyclic field extension of k, we give a combinatorial desc ...
Jerusalem2023The Nonvanishing Problem for varieties with nef anticanonical bundle
We prove that if (X, A) is a threefold pair with mild singularities such that -(KX + A) is nef, then the numerical class of -(KX + A) is effective. ...
Berlin2023Positivity 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 ...
2022Serre-Tate theory for Calabi-Yau varieties
Classical Serre-Tate theory describes deformations of ordinary abelian varieties. It implies that every such variety has a canonical lift to characteristic zero and equips the base of its universal deformation with a Frobenius lifting and canonical multipl ...
WALTER DE GRUYTER GMBH2021Ordinary varieties with trivial canonical bundle are not uniruled
Zsolt Patakfalvi, Maciej Emilian Zdanowicz
We prove that smooth, projective, K-trivial, weakly ordinary varieties over a perfect field of characteristic p>0 are not geometrically uniruled. We also show a singular version of our theorem, which is sharp in multiple aspects. Our work, together with La ...
2021Global Frobenius liftability I
We formulate a conjecture characterizing smooth projective varieties in positive characteristic whose Frobenius morphism can be lifted modulo p(2)-we expect that such varieties, after a finite stale cover, admit a toric fibration over an ordinary abelian v ...
EUROPEAN MATHEMATICAL SOC-EMS2021Positivity 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 HEIDELBERG2020