Luís Duarte: The initial ideal of a generic artinian Gorenstein algebra

Abstract: In this talk we will focus on how to compute the initial ideal of Ann(G) in two separate cases: when G is a generic form and when G is a complete symmetric form. It turns out that in the first case this initial ideal is generated by the largest possible monomials in each degree. For the second case, the answer is the same, if we consider the degree reverse lexicographic ordering, and in this situation we are actually able to determine a minimal Gröbner basis of the ideal. Moreover, we determine the total Betti numbers for a class of strongly stable monomial ideals and show that these numbers agree with those for the degree reverse lexicographical initial ideals of the ideal generated by a sufficiently large number of generic forms, and of the annihilator ideal of a generic form.