We construct smooth families of elliptic surface pairs with terminal singularities over a DVR of positive or mixed characteristic $(X,B)\to \mathrm{Spec}R$, such that $P_m(X_k,B_k)>P_m(X_K,B_K)$ for all sufficiently divisible $m>0$. In particular, this shows that invariance of all sufficiently divisible plurigenera does not follow from the MMP and Abundance Conjectures.Comment: Previous version contained a mistake, the result is now slightly weaker. Improved exposition. Comments welcom
We show that there exist smooth surfaces violating Generic Vanishing in any characteristic $p \geq 3...
We prove that any Fourier–Mukai partner of an abelian surface over an algebraically closed field of ...
We classify all prime thick subcategories in the derived category of coherent sheaves on elliptic cu...
We show the abundance theorem for arithmetic klt threefold pairs whose closed point have residue cha...
In this dissertation, we study the problem of the deformation invariance of plurigenera of algebraic...
This paper answers a question of Demailly whether a smooth family of nonsingular projective varietie...
We prove the abundance conjecture for projective slc surfaces over arbitrary fields of positive char...
The first author explicitly describes the set of Fourier--Mukai partners of elliptic ruled surfaces ...
The first author explicitly describes the set of Fourier--Mukai partners of elliptic ruled surfaces ...
In this paper, we classify Du Val del Pezzo surfaces of Picard rank one in positive characteristic. ...
We deduce an analogue of the Bogomolov conjecture for non-degenerate subvarieties in fibered product...
We study the space of rational curves on del Pezzo surfaces in positive characteristic. For most pri...
This paper resolves several outstanding questions regarding the Minimal Model Program for klt threef...
X. For L ample the Kodaira Vanishing Theorem says that H i(X,L−1) = 0, for i < dimX. Recall that...
Motivated by the question of properness of the moduli space of stable surfaces in mixed characterist...
We show that there exist smooth surfaces violating Generic Vanishing in any characteristic $p \geq 3...
We prove that any Fourier–Mukai partner of an abelian surface over an algebraically closed field of ...
We classify all prime thick subcategories in the derived category of coherent sheaves on elliptic cu...
We show the abundance theorem for arithmetic klt threefold pairs whose closed point have residue cha...
In this dissertation, we study the problem of the deformation invariance of plurigenera of algebraic...
This paper answers a question of Demailly whether a smooth family of nonsingular projective varietie...
We prove the abundance conjecture for projective slc surfaces over arbitrary fields of positive char...
The first author explicitly describes the set of Fourier--Mukai partners of elliptic ruled surfaces ...
The first author explicitly describes the set of Fourier--Mukai partners of elliptic ruled surfaces ...
In this paper, we classify Du Val del Pezzo surfaces of Picard rank one in positive characteristic. ...
We deduce an analogue of the Bogomolov conjecture for non-degenerate subvarieties in fibered product...
We study the space of rational curves on del Pezzo surfaces in positive characteristic. For most pri...
This paper resolves several outstanding questions regarding the Minimal Model Program for klt threef...
X. For L ample the Kodaira Vanishing Theorem says that H i(X,L−1) = 0, for i < dimX. Recall that...
Motivated by the question of properness of the moduli space of stable surfaces in mixed characterist...
We show that there exist smooth surfaces violating Generic Vanishing in any characteristic $p \geq 3...
We prove that any Fourier–Mukai partner of an abelian surface over an algebraically closed field of ...
We classify all prime thick subcategories in the derived category of coherent sheaves on elliptic cu...
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