Mathematische Annalen

, Volume 358, Issue 1–2, pp 143–168 | Cite as

Birational geometry of O’Grady’s six dimensional example over the Donaldson–Uhlenbeck compactification

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Abstract

We determine the birational geometry of O’Grady’s six dimensional example over the Donaldson–Uhlenbeck compactification, by looking at the locus of non-locally-free sheaves on the relevant moduli space.

Mathematics Subject Classification (2000)

14J60 37J35 

Notes

Acknowledgments

The author would like to thank Manfred Lehn for his suggestions. Several crucial ideas came out of the discussions with him. He would also like to thank Arvid Perego for stimulating discussions. The author is supported by Grant-in-Aid for Young Scientists (B) 22740004, the Ministry of Education, Culture, Sports, Science and Technology, Japan. At the time of writing the article, he was a member of Global COE program of Graduate School of Mathematics, the University of Tokyo.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  1. 1.Graduate School of Mathematical SciencesThe University of TokyoTokyoJapan
  2. 2.Department of Mathematics, Faculty of Science and EngineeringWaseda UniversityTokyoJapan

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