Research project Expecting unexpected relations

Concretely, we study the vector space dimension of the quotient of the polynomial ring in n variables with the ideal generated by m>= n+2 d-powers of general linear forms. One goal of the project is to understand this dimension in terms of the one obtained from m general forms of degree d and thus gain a deeper understanding of the Iarrobino-Fröberg conjecture. Another goal is to further develop the theory of fat points schemes.