Given a saturated ideal J of a zero-dimensional subscheme, irrelevant ideal irr, and a tuple A, resolveViaFatPoint computes a free resolution of J intersected with A-th power of the irrelevant ideal. See Theorem 4.1 of [BES, arXiv:1703.07631].
Below we follow example 4.7 of [BES,arXiv:1703.07631] and compute the virtual resolution of 6 points in ℙ1×ℙ1×ℙ2.
N = {1,1,2} |
pts = 6 |
(S, E) = productOfProjectiveSpaces N |
irr = intersect for n to #N-1 list (
ideal select(gens S, i -> (degree i)#n == 1)
); |
I = saturate intersect for i to pts - 1 list (
P := sum for n to N#0 - 1 list ideal random({1,0,0}, S);
Q := sum for n to N#1 - 1 list ideal random({0,1,0}, S);
R := sum for n to N#2 - 1 list ideal random({0,0,1}, S);
P + Q + R
); |
C = resolveViaFatPoint (I, irr, {2,1,0}) |
isVirtual(I, irr, C) |