Macaulay2 » Documentation
Packages » SectionRing :: isMRegular
next | previous | forward | backward | up | index | toc

isMRegular -- isMRegular(F,G,m) tests where F is m-regular with respect to G (globally generated) in the sense of Castelnuovo-Mumford. Omitting G assumes G=O_X(1).



isMRegular(F,G,m) tests definition 1.8.4 of Lazarsfeld's Positivity in Algebraic Geometry I, which is to say whether H^i(F \otimes G^(m-i)) = 0 for every i>0. It tests (in this order) H^1, H^2, \ldots, H^dim(X), and stops as soon as a non-zero cohomology is found. If none is found, F is m-G-regular, and it outputs true.

Ways to use isMRegular :

For the programmer

The object isMRegular is a method function.