In algebraic geometry, the Castelnuovo–Mumford regularity of a coherent sheaf F over projective space P n {\displaystyle \mathbf {P} ^{n}} is the smallest...

1999. Castelnuovo–Mumford regularity Mumford's compactness theorem Haboush's theorem Hilbert–Mumford criterion Stable mapping class group Mumford-Tate...

also known as the dragon curve sequence Regular tree grammar Castelnuovo–Mumford regularity of a coherent sheaf Closed regular sets in solid modeling Irregularity...

lecture. Castelnuovo proved it. In total, Castelnuovo published over 100 articles, books and memoirs. Castelnuovo curve Castelnuovo–Mumford regularity Castelnuovo...

constructed as a mapping cone of Eagon–Northcott complexes. The Castelnuovo–Mumford regularity may be read off the minimum resolution of the ideal I defining...

{O}}_{\mathbb {P} ^{n}}\to {\mathcal {O}}_{X}\to 0} Castelnuovo–Mumford regularity Hilbert scheme Quot scheme Ravi Vakil (2015). Foundations of...

points on K3 and a generalized Kummer surface. Quot scheme Castelnuovo–Mumford regularity Matsusaka's big theorem Moduli of algebraic curves Moduli space...

is invertible (locally free of rank one). Castelnuovo–Mumford regularity The Castelnuovo–Mumford regularity of a coherent sheaf F on a projective space...

a homogeneous ideal in a polynomial ring over a field, the Castelnuovo–Mumford regularity of the projective algebraic set defined by I is the minimal...

n_{0}} (depending on F {\displaystyle {\mathcal {F}}} ; see also Castelnuovo–Mumford regularity) such that H p ( X , F ( n ) ) = 0 {\displaystyle H^{p}(X,{\mathcal...

the global cohomology of projective schemes. For example, the Castelnuovo–Mumford regularity can be formulated using local cohomology as reg ( M ) = sup...

rings with this property are called absolutely flat. regularity Castelnuovo–Mumford regularity is an invariant of a graded module over a graded ring...

(algebraic geometry) Borel fixed-point theorem (algebraic geometry) Castelnuovo theorem (algebraic geometry) Cayley–Salmon theorem (algebraic surfaces)...