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

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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.
Original languageEnglish
Title of host publicationProceedings of Symposia in Pure Mathematics
Subtitle of host publicationAlgebraic Geometry: Salt Lake City 2015
PublisherAmerican Mathematical Society
Pages3-28
Volume97
ISBN (Print)978-1-4704-2754-2
Publication statusPublished - 2018
EventSummer Research Institute on Algebraic Geometry - University of Utah, Salt Lake City, United States
Duration: 13 Jul 201531 Jul 2015

Conference

ConferenceSummer Research Institute on Algebraic Geometry
CountryUnited States
CitySalt Lake City
Period13/07/1531/07/15

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