347 research outputs found
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
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