Problems with heft vectors in M2

asked 2014-09-05 15:49:05 -0500

bfitzpat gravatar image

updated 2015-01-14 03:09:01 -0500

FrédéricC gravatar image

I hope this question is on-topic on this forum.

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.

Does anyone happen to know of any workarounds in this situation?

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
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