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Mathematische Annalen

, Volume 319, Issue 4, pp 797–808 | Cite as

Frobenius splitting of Hilbert schemes of points on surfaces

  • Shrawan Kumar
  • Jesper Funch Thomsen
Original article

Abstract.

Let X be a quasiprojective smooth surface defined over an algebraically closed field of positive characteristic. In this note we show that if X is Frobenius split then so is the Hilbert scheme Hilb\(^n(X)\) of n points inX. In particular, we get the higher cohomology vanishing for ample line bundles on Hilb\(^n(X)\) when X is projective and Frobenius split.

Keywords

Smooth Surface Line Bundle Positive Characteristic Hilbert Scheme Ample Line Bundle 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2001

Authors and Affiliations

  • Shrawan Kumar
    • 1
  • Jesper Funch Thomsen
    • 2
  1. 1.Department of Mathematics, University of North Carolina, Chapel Hill, NC 27599-3250, USA (e-mail: kumar@math.unc.edu) US
  2. 2.Matematisk Institut, Aarhus Universitet, Ny Munkegade, DK-8000 århus C, Denmark (e-mail: funch@imf.au.dk) DK

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