I am working with the "NormalToricVarieties" package in M2.
Part of my research involves determining when the higher cohomology groups of certain twists of the structure sheaf of a toric variety vanish. I have a specific example where in computing HH^1(X,OO_X(1,1)) I am confronted with the following error:
stdio:8:3:(3): error: heft vector required that is positive on the degrees of the variables {0, 1, 2, 3, 4, 5, 6}
I know that this group should be trivial but somehow the absence of a heft vector is bothering the compiler. I'm not sure whether or not there is a way to get M2 to compute this group.
Do you happen to know of any workarounds in this situation? I'd greatly appreciate any insight you may have.
The example I am using is as follows:
loadPackage "NormalToricVarieties";
Rho = {
{ 0 , 0 , 0 , 0 , 1 }
, { 1 , 0 , 0 , 0 , 1 }
, { 0 , 1 , 0 , 0 , 1 }
, { 0 , 0 , 1 , 0 , 1 }
, { 0 , 0 , 0 , 1 , 1 }
, { -1 , -2 , -1 , -1 , 1 }
, { -2 , -1 , -1 , -1 , 1 }
};
Sigma = {
{ 2 , 3 , 4 , 5 , 6 }
, { 0 , 1 , 2 , 3 , 4 }
, { 0 , 1 , 2 , 3 , 5 }
, { 0 , 1 , 2 , 4 , 5 }
, { 0 , 1 , 3 , 4 , 5 }
, { 0 , 2 , 3 , 4 , 5 }
};
X = normalToricVariety(Rho,Sigma);
HH^2(X,OO_X(1,1)) -- HH^n for n=2 works fine
HH^1(X,OO_X(1,1)) -- HH^n for n=1 gives an error
