Castelnuovo–Mumford regularity

In algebraic geometry, the Castelnuovo–Mumford regularity of a coherent sheaf F over projective space P n {\displaystyle \mathbf {P} ^{n}} is the smallest integer r such that it is r-regular, meaning that H i ( P n , F ( r − i ) ) = 0 {\displaystyle H^{i}(\mathbf {P} ^{n},F(r-i))=0} whenever i > 0 {\displaystyle i>0} . The regularity of a subscheme is defined to be the regularity of its sheaf of ideals.

Source: Wikipedia — Castelnuovo–Mumford regularity (CC BY-SA 4.0)