Computing with jets (Q6103182)

This paper describes a package for the commutative algebra software system Macaulay2 for computation of the jet schemes of an affine algebraic variety. The explicit description of jet schemes is useful for the computation of invariants of singularities in algebraic geometry and commutative algebra, but such computations are often difficult to do by hand. This paper describes the implementation of the construction of jet schemes, as well as several more specific methods. These methods include the computation of the reduced jet schemes of varieties defined by monomial ideals, as well as their minimal primes and multiplities. This also includes algorithms for the jet schemes of a squarefree quadratric ideal associated to a (hyper)graph, and the corresponding graph of this jet scheme. Finally, the paper describes the computation of the defining equations for the principal component of the \(m\)-jet scheme (i.e., the irreducible component of the \(m\)-jet scheme of an irreducible variety obtained as the closure of the \(m\)-jets lying over smooth points). Example computations of the jet schemes of determinal varieties are given.