Concept
Kodaira dimension
Related publications (34)
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 ...
Hoboken2023Unlikely intersections on the p-adic formal ball
We investigate generalizations along the lines of the Mordell-Lang conjecture of the author's p-adic formal Manin-Mumford results for n-dimensional p-divisible formal groups F. In particular, given a finitely generated subgroup (sic) of F(Q(p)) and a close ...
SPRINGER INT PUBL AG2023A DONALDSON-THOMAS CREPANT RESOLUTION CONJECTURE ON CALABI-YAU 4-FOLDS
Let G be a finite subgroup of SU(4) such that its elements have age at most one. In the first part of this paper, we define K-theoretic stable pair invariants on a crepant resolution of the affine quotient C4/G, and conjecture a closed formula for their ge ...
Providence2023The Jordan property for local fundamental groups
Stefano Filipazzi, Roberto Svaldi
We show the Jordan property for regional fundamental groups of klt singularities of fixed dimension. Furthermore, we prove the existence of effective simultaneous index 1 covers for n-dimensional klt singularities. We give an application to the study of lo ...
2022The Lang-Trotter conjecture for products of non-CM elliptic curves
Inspired by the work of Lang-Trotter on the densities of primes with fixed Frobenius traces for elliptic curves defined over Q and by the subsequent generalization of Cojocaru-Davis-Silverberg-Stange to generic abelian varieties, we study the analogous que ...
SPRINGER2022On 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 PUBL2022On the projectivity of some moduli spaces of varieties
Quentin Arthur Frantisek Posva
This thesis is constituted of one article and three preprints that I wrote during my PhD thesis. Their common theme is the moduli theory of algebraic varieties. In the first article I study the Chow--Mumford line bundle for families of uniformly K-stable F ...
EPFL2022On the Mordell-Weil lattice of y(2) = x(3) + bx plus t(3n+1) in characteristic 3
We study the elliptic curves given by y(2) = x(3) + bx + t(3n+1) over global function fields of characteristic 3 ; in particular we perform an explicit computation of the L-function by relating it to the zeta function of a certain superelliptic curve u(3) ...
SPRINGER INT PUBL AG2022On the Kodaira vanishing theorem for log del Pezzo surfaces in positive characteristic
We investigate the vanishing of H1(X,OX(−D)) for a big and nef Q-Cartier Z-divisor D on a log del Pezzo pair (X,Δ) over a perfect field of positive characteristic p. ...
2021Ordinary 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 ...
2021