Birational geometry of moduli spaces of sheaves and Bridgeland stability

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Abstract

Moduli spaces of sheaves and Hilbert schemes of points have experienced a recent resurgence in interest in the past several years, due largely to new techniques arising from Bridgeland stability conditions and derived category methods. In particular, classical questions about the birational geometry of these spaces can be answered by using new tools such as the positivity lemma of Bayer and Macri`. In this article we first survey classical results on moduli spaces of sheaves and their birational geometry. We then discuss the relationship between these classical results and the new techniques coming from Bridgeland stability, and discuss how cones of ample divisors on these spaces can be computed with these new methods. This survey expands upon the author's talk at the 2015 Bootcamp in Algebraic Geometry preceding the 2015 AMS Summer Research Institute on Algebraic Geometry at the University of Utah.

Original languageEnglish (US)
Title of host publicationSurveys on recent developments in algebraic geometry
Subtitle of host publicationbootcamp for the Summer Research Institute on Algebraic Geometry, 2015
EditorsIzzet Coskun, Tommaso de Fernex, Angela Gibney
PublisherAmerican Mathematical Society
Pages101-148
Number of pages48
ISBN (Electronic)9781470441210
ISBN (Print)9781470435578
DOIs
StatePublished - Jan 1 2017
EventSurveys on recent developments in algebraic geometry : bootcamp for the Summer Research Institute on Algebraic Geometry, 2015 - Salt Lake City, United States
Duration: Jul 6 2015Jul 10 2015

Publication series

NameProceedings of Symposia in Pure Mathematics
Volume95
ISSN (Print)0082-0717

Other

OtherSurveys on recent developments in algebraic geometry : bootcamp for the Summer Research Institute on Algebraic Geometry, 2015
CountryUnited States
CitySalt Lake City
Period7/6/157/10/15

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All Science Journal Classification (ASJC) codes

  • Mathematics(all)

Cite this

Huizenga, J. (2017). Birational geometry of moduli spaces of sheaves and Bridgeland stability. In I. Coskun, T. D. Fernex, & A. Gibney (Eds.), Surveys on recent developments in algebraic geometry: bootcamp for the Summer Research Institute on Algebraic Geometry, 2015 (pp. 101-148). (Proceedings of Symposia in Pure Mathematics; Vol. 95). American Mathematical Society. https://doi.org/10.1090/pspum/095/01639