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3 results

  • Smash nilpotent cycles on varieties dominated by products of curves

  • Part of
  • Ronnie Sebastian
  • Journal:
    Compositio Mathematica / Volume 149 / Issue 9 / September 2013
    Published online by Cambridge University Press:
    28 June 2013, pp. 1511-1518
    Print publication:
    September 2013
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  • Voevodsky conjectured that numerical equivalence and smash equivalence coincide on a smooth projective variety. We prove the conjecture for 1-cycles on varieties dominated by products of curves.

  • Varieties with ample cotangent bundle

  • Olivier Debarre
  • Journal:
    Compositio Mathematica / Volume 141 / Issue 6 / November 2005
    Published online by Cambridge University Press:
    04 December 2007, pp. 1445-1459
    Print publication:
    November 2005
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  • The aim of this article is to provide methods for constructing smooth projective complex varieties with ample cotangent bundle. We prove that the intersection of at least n/2 sufficiently ample general hypersurfaces in a complex abelian variety of dimension n has ample cotangent bundle. We also discuss analogous questions for complete intersections in the projective space. Finally, we present an unpublished result of Bogomolov which states that a general linear section of small dimension of a product of sufficiently many smooth projective varieties with big cotangent bundle has ample cotangent bundle.