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

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...

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

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...

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...

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

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

variables) Casey's theorem (Euclidean geometry) Castelnuovo theorem (algebraic geometry) Castelnuovo–de Franchis theorem (algebraic geometry) Castigliano's...