Timeline for rational effective implies effective?
Current License: CC BY-SA 3.0
7 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Apr 3, 2017 at 1:56 | answer | added | user41650 | timeline score: 2 | |
| Mar 15, 2017 at 21:49 | comment | added | Junyan Xu | A side question is whether the effective monoid is also generated by (-1) and (-2)-curves; this is false for degree 1 genuine del Pezzo surfaces, but I am yet to see another counterexample. | |
| Mar 15, 2017 at 21:35 | comment | added | Junyan Xu | I still think that it can be effectively determined whether a finitely generated monoid is saturated given its generators, but I don't know about an algorithm. Maybe people working in toric varieties know where such an algorithm is implemented... | |
| Mar 15, 2017 at 21:35 | comment | added | Junyan Xu | @gbp We know that the effective cone is generated by (-1) and (-2)-curves (d≤7) from arxiv.org/pdf/math/0703202.pdf (Theorem 3.10) The paper arxiv.org/pdf/math/0604194.pdf gives generators of Cox rings and hence generators of effective monoids. However, I don't see what the question has to do with primitivity of generators. The group generated by two primitive vectors in Z^2 need not be saturated, and even when the group is saturated, the monoid they generate need not be saturated (e.g. (0,1) doesn't lie in the monoid generated by (1,0) and (-1,2)). | |
| Mar 15, 2017 at 21:34 | comment | added | user41650 | @gbp Thanks, could you turn your comments on del pezzo surface case into an answer? I dont see how the "generators are primitive" will imply this statement | |
| Mar 15, 2017 at 13:50 | comment | added | Chen Jiang | If $X$ is assumed to be del Pezzo, this is okay, right? | |
| Mar 14, 2017 at 0:03 | history | asked | user41650 | CC BY-SA 3.0 |