@inproceedings{da13457d42b34328bfff161393a79a83,
title = "The moduli spaces of sheaves on surfaces, pathologies and brill-noether problems",
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.",
author = "Izzet Coskun and Jack Huizenga",
note = "Funding Information: Acknowledgements The first author would like to thank the organizers of the Abel Symposium, J.A. Christophersen, J. C. Ottem, R. Piene, K. Ranestad, and S. Tirabassi, for a wonderful conference and their hospitality. We have benefitted from many discussions with A. Bayer, A. Bertram, L. Ein, J. Kopper, E. Macr{\`i}, H. Nuer, B. Schmidt, M. Woolf and K. Yoshioka. During the preparation of this article the first author was partially supported by the NSF grant DMS-1500031 and NSF FRG grant DMS 1664296 and the second author was partially supported by the NSA Young Investigator Grant H98230-16-1-0306 and NSF FRG grant DMS 1664303. Publisher Copyright: {\textcopyright} Springer Nature Switzerland AG 2018.; Abel Symposium on Geometry of Moduli, 2017 ; Conference date: 07-08-2017 Through 11-08-2017",
year = "2018",
doi = "10.1007/978-3-319-94881-2_4",
language = "English (US)",
isbn = "9783319948805",
series = "Abel Symposia",
publisher = "Springer Heidelberg",
pages = "75--105",
editor = "Christophersen, {Jan Arthur} and Kristian Ranestad",
booktitle = "Geometry of Moduli",
address = "Germany",
}