The Space of Stability Conditions on Abelian Threefolds, and on some Calabi-Yau Threefolds

We describe a connected component of the space of stability conditions on abelian threefolds, and on Calabi-Yau threefolds obtained as (the crepant resolution of) a finite quotient of an abelian threefold. Our proof includes the following essential steps: 1. We simultaneously strengthen a conjecture by the first two authors and Toda, and prove that it follows from a more natural and seemingly weaker statement. This conjecture is a Bogomolov-Gieseker type inequality involving the third Chern character of "tilt-stable" two-term complexes on smooth projective threefolds; we extend it from complexes of tilt-slope zero to arbitrary tilt-slope. 2. We show that this stronger conjecture implies the so-called support property of Bridgeland stability conditions, and the existence of an explicit open subset of the space of stability conditions. 3. We prove our conjecture for abelian threefolds, thereby giving reproving and generalizing a result by Maciocia and Piyaratne. Important in our approach is a more systematic understanding on the behaviour of quadratic inequalities for semistable objects under wall-crossing, closely related to the support property.Comment: 45 pages, 1 figure. v2: addressed referee comments. To appear in Inventiones Mat

On the intersection of ACM curves in \PP^3

Bezout's theorem gives us the degree of intersection of two properly intersecting projective varieties. As two curves in P^3 never intersect properly, Bezout's theorem cannot be directly used to bound the number of intersection points of such curves. In this work, we bound the maximum number of intersection points of two integral ACM curves in P^3. The bound that we give is in many cases optimal as a function of only the degrees and the initial degrees of the curves

Ulrich bundles on non-special surfaces with pg=0p_g=0 p g = 0 and q=1q=1 q = 1

Let S be a surface with pg(S) = 0 , q(S) = 1 and endowed with a very ample line bundle OS(h) such that h1(S, OS(h)) = 0. We show that such an S supports families of dimension p of pairwise non-isomorphic, indecomposable, Ulrich bundles for arbitrary large p. Moreover, we show that S supports stable Ulrich bundles of rank 2 if the genus of the general element in | h| is at least 2

Pet roundworms and hookworms: a continuing need for global worming

Abstract Ascarids and ancylostomatids are the most important parasites affecting dogs and cats worldwide, in terms of diffusion and risk for animal and human health. Different misconceptions have led the general public and pet owners to minimize the importance of these intestinal worms. A low grade of interest is also registered among veterinary professions, although there is a significant merit in keeping our guard up against these parasites. This article reviews current knowledge of ascarids and ancylostomatids, with a special focus on pathogenicity, epidemiology and control methods in veterinary and human medicine.</p