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 ...
Let X be a complex projective K3 surface and let T-X be its transcendental lattice; the characteristic polynomials of isometries of T-X induced by automorphisms of X are powers of cyclotomic polynomials. Which powers of cyclotomic polynomials occur? The ai ...
We prove that there are finitely many families, up to isomorphism in codimension one, of elliptic Calabi-Yau manifolds Y -> X with a rational section, provided that dim(Y)
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 ...
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 ...
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 ...
Secondary electron emission (SEE) of solid materials due to electron bombardment is influenced by numerous properties of materials, where the surface condition plays a critical role in the value of secondary electron yield (SEY). Here, a 3D random microstr ...
While over fields of characteristic at least 5, a normal, projective and Gorenstein del Pezzo surface is geometrically normal, this does not hold for characteristic 2 and 3. There is no characterization of all such non-geometrically normal surfaces, but th ...
Emergence of products that feature functional surfaces with complex geometries, such as freeform optics in consumer electronics and augmented reality and virtual reality, requires high-accuracy non-contact surface measurement. However, large discrepancies ...
In this article we prove two cases of the abundance conjecture for 3-folds in characteristic p>5: (i) (X,Delta) is klt and kappa(X,KX+Delta)=1, and (ii) (X,Delta) is klt, KX+Delta equivalent to 0 and X is not uniruled. ...
The objective of this series is to study metric geometric properties of disjoint unions of Cayley graphs of amenable groups by group properties of the Cayley accumulation points in the space of marked groups. In this Part II, we prove that a disjoint union ...
We show that for a surjective, separable morphism f of smooth projective varieties over a field of positive characteristic such that f(*) OX congruent to O-Y subadditivity of Kodaira dimension holds, provided the base is of general type and the Hasse-Witt ...
We compute the L-2-Betti numbers of the free C*-tensor categories, which are the representation categories of the universal unitary quantum groups A(u)(F). We show that the L-2-Betti numbers of the dual of a compact quantum group G are equal to the L-2-Bet ...
We prove that the number of rational points of bounded height on certain del Pezzo surfaces of degree 1 defined over Q grows linearly, as predicted by Manin's conjecture. ...
Ceramic surface microstructuring is a rapidly growing field with a variety of applications in tribology, wetting, biology, and so on. However, there are limitations to large-area microstructuring and fabrication of three-dimensional (3D) micro free forms. ...
We state conditions under which the set S(k) of k-rational points on a del Pezzo surface S of degree 1 over an infinite field k of characteristic not equal to 2 or 3 is Zariski dense. For example, it suffices to require that the elliptic fibration S -> P-1 ...
We show that Brauer classes of a locally solvable degree 4 del Pezzo surface X are vertical for some projection away from a plane g : X -> P-1, i.e., that every Brauer class is obtained by pullback from an element of Br k(P-1). As a consequence, we prove t ...
We compute L-2-Betti numbers of postliminal, locally compact, unimodular groups in terms of ordinary dimensions of reduced cohomology with coefficients in irreducible unitary representations and the Plancherel measure. This allows us to compute the L-2-Bet ...
We consider a notion of balanced metrics for triples (X, L, E) which depend on a parameter alpha, where X is a smooth complex manifold with an ample line bundle L and E is a holomorphic vector bundle over X. For generic choice of alpha, we prove that the l ...
