English

Wall-Crossing implies Brill-Noether. Applications of stability conditions on surfaces

Algebraic Geometry 2016-10-20 v2

Abstract

Over the last few years, wall-crossing for Bridgeland stability conditions has led to a large number of results in algebraic geometry, particular on birational geometry of moduli spaces. We illustrate some of the methods behind these result by reproving Lazarsfeld's Brill-Noether theorem for curves on K3 surfaces via wall-crossing. We conclude with a survey of recent applications of stability conditions on surfaces. The intended reader is an algebraic geometer with a limited working knowledge of derived categories. This article is based on the author's talk at the AMS Summer Institute on Algebraic Geometry in Utah, July 2015.

Keywords

Cite

@article{arxiv.1604.08261,
  title  = {Wall-Crossing implies Brill-Noether. Applications of stability conditions on surfaces},
  author = {Arend Bayer},
  journal= {arXiv preprint arXiv:1604.08261},
  year   = {2016}
}

Comments

25 pages, 3.5 figures. v2: expanded comparison to Lazarsfeld's methods and results; addressed referee comments