Access

You are not currently logged in.

Access your personal account or get JSTOR access through your library or other institution:

login

Log in to your personal account or through your institution.

If You Use a Screen Reader

This content is available through Read Online (Free) program, which relies on page scans. Since scans are not currently available to screen readers, please contact JSTOR User Support for access. We'll provide a PDF copy for your screen reader.

Geometric Invariant Theory and Flips

Michael Thaddeus
Journal of the American Mathematical Society
Vol. 9, No. 3 (Jul., 1996), pp. 691-723
Stable URL: http://www.jstor.org/stable/2152810
Page Count: 33
  • Read Online (Free)
  • Download ($30.00)
  • Subscribe ($19.50)
  • Cite this Item
Since scans are not currently available to screen readers, please contact JSTOR User Support for access. We'll provide a PDF copy for your screen reader.
Preview not available

Abstract

We study the dependence of geometric invariant theory quotients on the choice of a linearization. We show that, in good cases, two such quotients are related by a flip in the sense of Mori, and explain the relationship with the minimal model program. Moreover, we express the flip as the blow-up and blow-down of specific ideal sheaves, leading, under certain hypotheses, to a quite explicit description of the flip. We apply these ideas to various familiar moduli problems, recovering results of Kirwan, Boden-Hu, Bertram-Daskalopoulos-Wentworth, and the author. Along the way we display a chamber structure, following Duistermaat-Heckman, on the space of all linearizations. We also give a new, easy proof of the Bialynicki-Birula decomposition theorem.

Page Thumbnails

  • Thumbnail: Page 
691
    691
  • Thumbnail: Page 
692
    692
  • Thumbnail: Page 
693
    693
  • Thumbnail: Page 
694
    694
  • Thumbnail: Page 
695
    695
  • Thumbnail: Page 
696
    696
  • Thumbnail: Page 
697
    697
  • Thumbnail: Page 
698
    698
  • Thumbnail: Page 
699
    699
  • Thumbnail: Page 
700
    700
  • Thumbnail: Page 
701
    701
  • Thumbnail: Page 
702
    702
  • Thumbnail: Page 
703
    703
  • Thumbnail: Page 
704
    704
  • Thumbnail: Page 
705
    705
  • Thumbnail: Page 
706
    706
  • Thumbnail: Page 
707
    707
  • Thumbnail: Page 
708
    708
  • Thumbnail: Page 
709
    709
  • Thumbnail: Page 
710
    710
  • Thumbnail: Page 
711
    711
  • Thumbnail: Page 
712
    712
  • Thumbnail: Page 
713
    713
  • Thumbnail: Page 
714
    714
  • Thumbnail: Page 
715
    715
  • Thumbnail: Page 
716
    716
  • Thumbnail: Page 
717
    717
  • Thumbnail: Page 
718
    718
  • Thumbnail: Page 
719
    719
  • Thumbnail: Page 
720
    720
  • Thumbnail: Page 
721
    721
  • Thumbnail: Page 
722
    722
  • Thumbnail: Page 
723
    723