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Conjecture

Fujita Conjecture

Algebraic Geometry

Fujita's conjecture is a problem in the theories of algebraic geometry and complex manifolds, named after the Japanese mathematician Takao Fujita, who formulated it in 1985.

Facts
Statement
For a positive holomorphic line bundle L on a compact complex manifold M of complex dimension n, the bundle K_M tensor L to the power m is spanned by sections when m is at least n plus 1. 1
Proposed Year
1985 1
Progress Toward Resolution
Ein and Lazarsfeld proved in 1993 the first part of the Fujita conjecture, that m at least 4 implies global generation, for three dimensional varieties. 1
Classification
Resolution Status
Open 1
Prize Status
Prize Status (category)
No Prize Offered 1
Connections

In Branch

Source Fujita Conjecture, Wikipedia
Sources
1. Fujita Conjecture, Wikipedia
  • Statement section
    spanned by sections when m >= n + 1
  • Introduction section, second sentence
    It is named after Takao Fujita, who formulated it in 1985.
  • Known cases section
    Ein and Lazarsfeld in 1993 proved the first part of the Fujita conjecture, i.e. that m >= 4 implies global generation.
  • Lead section
  • In Branch: Algebraic Geometry, Lead sentence
    jita's conjecture is a problem in the theories of algebraic geometry and complex manifolds.
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