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- Castelnuovo–Mumford_regularity abstract "In algebraic geometry, the Castelnuovo–Mumford regularity of a coherent sheaf F over projective space Pn is the smallest integer r such that it is r-regular, meaning thatwhenever i > 0. The regularity of a subscheme is defined to be the regularity of its sheaf of ideals. The regularity controls when the Hilbert function of the sheaf becomes a polynomial; more precisely dim H0(Pn, F(m)) is a polynomial in m when m is at least the regularity. The concept of r-regularity was introduced by Mumford (1966, lecture 14), who attributed the following results to Guido Castelnuovo: An r-regular sheaf is s-regular for any s ≥ r.If a coherent sheaf is r-regular then F(r) is generated by its global sections.".
- Castelnuovo–Mumford_regularity wikiPageID "24560170".
- Castelnuovo–Mumford_regularity wikiPageRevisionID "569337673".
- Castelnuovo–Mumford_regularity authorlink "David Mumford".
- Castelnuovo–Mumford_regularity last "Mumford".
- Castelnuovo–Mumford_regularity loc "lecture 14".
- Castelnuovo–Mumford_regularity year "1966".
- Castelnuovo–Mumford_regularity subject Category:Algebraic_geometry.
- Castelnuovo–Mumford_regularity comment "In algebraic geometry, the Castelnuovo–Mumford regularity of a coherent sheaf F over projective space Pn is the smallest integer r such that it is r-regular, meaning thatwhenever i > 0. The regularity of a subscheme is defined to be the regularity of its sheaf of ideals. The regularity controls when the Hilbert function of the sheaf becomes a polynomial; more precisely dim H0(Pn, F(m)) is a polynomial in m when m is at least the regularity.".
- Castelnuovo–Mumford_regularity label "Castelnuovo–Mumford regularity".
- Castelnuovo–Mumford_regularity sameAs Castelnuovo%E2%80%93Mumford_regularity.
- Castelnuovo–Mumford_regularity sameAs Q5049716.
- Castelnuovo–Mumford_regularity sameAs Q5049716.
- Castelnuovo–Mumford_regularity wasDerivedFrom Castelnuovo–Mumford_regularity?oldid=569337673.