Skip to main content Accessibility help

We use cookies to distinguish you from other users and to provide you with a better experience on our websites. Close this message to accept cookies or find out how to manage your cookie settings.

Close cookie message
×
  1. Home
  2. Search

Refine search

Refine search

Access:
Content type:
Publication date:
Apply   From and To filters
Subject: Show more
Journals Show more
Publishers: Show more
Societies Show more
Series: Show more
Collections: Show more

Actions for selected content:

Select all | Deselect all
  • View selected items
  • Export citations
  • Download PDF (zip)
  • Save to Kindle
  • Save to Dropbox
  • Save to Google Drive

Save Search

You can save your searches here and later view and run them again in "My saved searches".

Please provide a title, maximum of 40 characters.
Cancel
×

2 results

  • Quasi-elementary contractions of Fano manifolds

  • Part of
  • Cinzia Casagrande
  • Journal:
    Compositio Mathematica / Volume 144 / Issue 6 / November 2008
    Published online by Cambridge University Press:
    01 November 2008, pp. 1429-1460
    Print publication:
    November 2008
    • Article
      • You have access
    • PDF
    • Export citation

  • Let X be a smooth complex Fano variety. We study ‘quasi-elementary’ contractions of fiber type of X, which are a natural generalization of elementary contractions of fiber type. If f:X→Y is such a contraction, then the Picard numbers satisfy ρX≤ρY+ρF, where F is a general fiber of f. We show that, if dim Y ≤3 and ρY≥4, then Y is smooth and Fano; if moreover ρY≥6, then X is a product. This yields sharp bounds on ρX when dim X=4 and X has a quasi-elementary contraction of fiber type, and other applications in higher dimensions.

  • The Noether–Lefschetz Theorem Via Vanishing of Coherent Cohomology

  • G. V. Ravindra
  • Journal:
    Canadian Mathematical Bulletin / Volume 51 / Issue 2 / 01 June 2008
    Published online by Cambridge University Press:
    20 November 2018, pp. 283-290
    Print publication:
    01 June 2008
    • Article
      • You have access
    • PDF
    • Export citation

  • We prove that for a generic hypersurface in ${{\mathbb{P}}^{2n+1}}$ of degree at least $2\,+\,2/n$, the $n$-th Picard number is one. The proof is algebraic in nature and follows from certain coherent cohomology vanishing.