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. ...
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 ...
We construct a modular desingularisation of (M) over bar (2,n)(P-r, d)(main). The geometry of Gorenstein singularities of genus two leads us to consider maps from prestable admissible covers; with this enhanced logarithmic structure, it is possible to desi ...
We discuss criteria for a stable map of genus two and degree 4 to the projective plane to be smoothable, as an application of our modular desingularisation of (M) over bar (2,n)(P-r, d)(main) via logarithmic geometry and Gorenstein singularities. ...
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 ...
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 ...
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 H1(X,OX(−D)) for a big and nef Weil divisor D on a normal projective variety w ...
We further the classification of rational surface singularities. Suppose (S, n, k) is a 3-dimensional strictly Henselian regular local ring of mixed characteristic (0, p > 5). We classify functions f for which S/(f) has an isolated rational singularity at ...
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 ...
Abelian varieties are fascinating objects, combining the fields of geometry and arithmetic. While the interest in abelian varieties has long time been of purely theoretic nature, they saw their first real-world application in cryptography in the mid 1980's ...
