How big can be the multiprojective variety for which Macaulay2 can calculate irreducible components and check their smoothness?
I have a multiprojective variety X in a product of projective spaces given by a multigraded ideal I. Suppose that the multiprojective variety is embedded into product of projective spaces the sum of whose dimensions is a and the number of generators of the ideal I is b. For which a and b can Macaulay2 in principle compute irreducible components of X and check for one of them if it is smooth (I think I can run Macaulay2 on a supercomputer)?
I don't know, have you tried it? You might want to provide your ideal I if you want a meaningful answer.