Timeline for Decompose a big divisor as nef big divisor and effective divisor

7 events

when toggle format	what		by	license	comment
Oct 10, 2014 at 3:29	history	edited	aegbert	CC BY-SA 3.0	added 84 characters in body
Oct 10, 2014 at 3:22	history	edited	aegbert	CC BY-SA 3.0	added 65 characters in body
Oct 10, 2014 at 2:51	history	edited	aegbert	CC BY-SA 3.0	added 20 characters in body
Oct 10, 2014 at 2:27	history	edited	aegbert	CC BY-SA 3.0	added 74 characters in body
Oct 10, 2014 at 0:45	comment	added	user47305		Does such $m$ even exist on a fixed variety $X$? I don't see that it's even true that there exists a constant $m = m(X)$ such that $h^0(mD) > 0$ if $D$ is big and Cartier on $X$; for $h^0(mD-A)$ it's even worse. I doubt a sequence of such $D$ is going to have the decompositions you want.
Oct 9, 2014 at 15:37	comment	added	Li Yutong		No, because I need $m$ does not depend on particular choice of $X$. Even in simpler case, where $D$ itself is Cartier, using the proof of Kodaira lemma (just as you did), I do not know if there is a universal $m$ such that $h^0(mD -A)$ is non-vanishing (where $A$ is an ample divisor).
Oct 9, 2014 at 15:16	history	answered	aegbert	CC BY-SA 3.0