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

2016/04/27 by Bayer, Arend · 5 citations
#14D20 #14E30 #14H51 #14J28 #18E30 #Algebraic Geometry (math.AG) #FOS: Mathematics

paper · doi:10.48550/arxiv.1604.08261

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.

Cited by

• Derived category of coherent systems on curves and stability conditions
• Bridgeland stability conditions on some higher-dimensional Calabi--Yau manifolds and generalized Kummer varieties
• Stability conditions on Calabi-Yau threefolds via Brill-Noether theory of curves
• More birational involutions
• Abel maps for integral curves via a derived perspective

Related

• An interesting wall-crossing: Failure of the wall-crossing/MMP correspondence
• Bridgeland-Stable Moduli Spaces for K-Trivial Surfaces
• The unreasonable effectiveness of wall-crossing in algebraic geometry
• Some examples of moduli spaces on surfaces via wall-crossing
• Mukai's Program (reconstructing a K3 surface from a curve) via wall-crossing, II