Non-Koszul syzygies of bihomogeneous polynomials

A DICKENSTEIN

Seminario; Commutative Algebra Seminar; 2017

Stockholm University

Fix a positive bidegree d  and let I be an ideal generated by three bihomogeneouspolynomials of bidegree d without common zeros in P^1 x P^1. In joint work withNicolas Botbol and Hal Schenck, we study the possible minimal free resolutionsof I.  We show that there are many possibleresolutions.In case the given polynomials are generic, we have aconjecture for the dimension of the non-Koszul syzygies in any bidegree thatexplains all computations. On the other side, Ralf Fr\"oberg has aconjecture for the dimension of the quotient by I in any bidegree. I willdiscuss theequivalence of these two conjectures