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
StatementFor 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 Progress Toward ResolutionEin 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 Prize Status
Prize Status (category) 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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