The moduli spaces of sheaves on surfaces, pathologies and brill-noether problems

Izzet Coskun, Jack Huizenga

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract

Brill-Noether Theorems play a central role in the birational geometry of moduli spaces of sheaves on surfaces. This paper surveys recent work on the Brill-Noether problem for rational surfaces. In order to highlight some of the difficulties for more general surfaces, we show that moduli spaces of rank 2 sheaves on very general hypersurfaces of degree d in ℙ3 can have arbitrarily many irreducible components as d tends to infinity.

Original languageEnglish (US)
Title of host publicationGeometry of Moduli
EditorsJan Arthur Christophersen, Kristian Ranestad
PublisherSpringer Heidelberg
Pages75-105
Number of pages31
ISBN (Print)9783319948805
DOIs
Publication statusPublished - Jan 1 2018
EventAbel Symposium on Geometry of Moduli, 2017 - Svolvær, Norway
Duration: Aug 7 2017Aug 11 2017

Publication series

NameAbel Symposia
Volume14
ISSN (Print)2193-2808
ISSN (Electronic)2197-8549

Other

OtherAbel Symposium on Geometry of Moduli, 2017
CountryNorway
CitySvolvær
Period8/7/178/11/17

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All Science Journal Classification (ASJC) codes

  • Mathematics(all)

Cite this

Coskun, I., & Huizenga, J. (2018). The moduli spaces of sheaves on surfaces, pathologies and brill-noether problems. In J. A. Christophersen, & K. Ranestad (Eds.), Geometry of Moduli (pp. 75-105). (Abel Symposia; Vol. 14). Springer Heidelberg. https://doi.org/10.1007/978-3-319-94881-2_4