Computing the Walls Associated to Bridgeland Stability Conditions on Projective Surfaces

We derive constraints on the existence of walls for Bridgeland stability conditions for general projective surfaces. We show that in suitable planes of stability conditions the walls are bounded and derive conditions for when the number of walls is globally finite. In examples, we show how to use the explicit conditions to locate walls and sometimes to show that there are no walls at all.Comment: 18 pages, 2 figures. A lot of tidying up following referee's comments especially in section 3. To appear in Asian J. Mat

A Fourier-Mukai Approach to the Enumerative Geometry of Principally Polarized Abelian Surfaces

We study twisted ideal sheaves of small length on an irreducible principally polarized abelian surface (T,l). Using Fourier-Mukai techniques we associate certain jumping schemes to such sheaves and completely classify such loci. We give examples of applications to the enumerative geometry of T and show that no smooth genus 5 curve on such a surface can contain a g^1_3. We also describe explicitly the singular divisors in the linear system |2l|.Comment: 21 pages with appendix, typos fixe

Generalized Fourier-Mukai Transforms

The paper sets out a generalized framework for Fourier-Mukai transforms and illustrates their use via vector bundle transforms. A Fourier-Mukai transform is, roughly, an isomorphism of derived categories of (sheaves) on smooth varieties X and Y. We show that these can only exist if the first Chern class of the varieties vanishes and, in the case of vector bundle transforms, will exist if and only if there is a bi-universal bundle on XxY which is "strongly simple" in a suitable sense. Some applications are given to abelian varieties extending the work of Mukai.Comment: 13 pages, AMSLaTeX 1.

An International Exchange Program: Self-Esteem Building and Relationship Development for Youth and Staff

Troubled youth can manage, and benefit from, short intensive relationship-centered experiences. This article reports on an innovative staff and client exchange program involving groups from Montreal, Quebec and Washington, D.C. Such experiences, as well as enhancing the youths\u27 cultural awareness and self-esteem, provide exciting staff-development opportunities

Rank One Bridgeland Stable Moduli Spaces on A Principally Polarized Abelian Surface

We compute moduli spaces of Bridgeland stable objects on an irreducible principally polarized complex abelian surface corresponding to twisted ideal sheaves. We use Fourier-Mukai techniques to extend the ideas of Arcara and Bertram to express wall-crossings as Mukai flops and show that the moduli spaces are projective.Comment: 17 pages, 3 figure