Symmetric tensors and geometry of ℙN subvarieties

Fedor Bogomolov, Bruno De Oliveira

Research output: Contribution to journalArticlepeer-review


This paper using a geometric approach produces vanishing and nonvanishing results concerning the spaces of twisted symmetric differentials H 0(X, SmΩX1 ⊗ script OX(k)) on subvarieties X ⊂ ℙN, with k ≤ m. Emphasis is given to the case of k = m which is special and whose nonvanishing results on the dimensional range dim X > 2/3(N - 1) are related to the space of quadrics containing X and the variety of all tangent trisecant lines of X. The paper ends with an application showing that the twisted symmetric plurigenera, Qα,m(Xt) = dim Η0(X, SmXt1 ⊗ αKXt)) along smooth families of projective varieties Xt are not invariant even for α arbitrarily large.

Original languageEnglish (US)
Pages (from-to)637-656
Number of pages20
JournalGeometric and Functional Analysis
Issue number3
StatePublished - Sep 2008


  • Quadrics
  • Symmetric differentials
  • Trisecant variety
  • Vanishing and nonvanishing theorems

ASJC Scopus subject areas

  • Analysis
  • Geometry and Topology


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