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

Izzet Coskun, Jack William 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
StatePublished - 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

Fingerprint

Noether
Sheaves
Moduli Space
Noether's theorem
Rational Surface
Irreducible Components
Hypersurface
Infinity
Tend

All Science Journal Classification (ASJC) codes

  • Mathematics(all)

Cite this

Coskun, I., & Huizenga, J. W. (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
Coskun, Izzet ; Huizenga, Jack William. / The moduli spaces of sheaves on surfaces, pathologies and brill-noether problems. Geometry of Moduli. editor / Jan Arthur Christophersen ; Kristian Ranestad. Springer Heidelberg, 2018. pp. 75-105 (Abel Symposia).
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Coskun, I & Huizenga, JW 2018, The moduli spaces of sheaves on surfaces, pathologies and brill-noether problems. in JA Christophersen & K Ranestad (eds), Geometry of Moduli. Abel Symposia, vol. 14, Springer Heidelberg, pp. 75-105, Abel Symposium on Geometry of Moduli, 2017, Svolvær, Norway, 8/7/17. https://doi.org/10.1007/978-3-319-94881-2_4

The moduli spaces of sheaves on surfaces, pathologies and brill-noether problems. / Coskun, Izzet; Huizenga, Jack William.

Geometry of Moduli. ed. / Jan Arthur Christophersen; Kristian Ranestad. Springer Heidelberg, 2018. p. 75-105 (Abel Symposia; Vol. 14).

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

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Coskun I, Huizenga JW. The moduli spaces of sheaves on surfaces, pathologies and brill-noether problems. In Christophersen JA, Ranestad K, editors, Geometry of Moduli. Springer Heidelberg. 2018. p. 75-105. (Abel Symposia). https://doi.org/10.1007/978-3-319-94881-2_4