Giovedì 2 maggio alle 16:30, nell’aula E al terzo livello del Dipartimento di Matematica e Applicazioni, la Prof. Emanuela De Negri (Università di Genova) terrà un seminario di Algebra Commutativa su

“ON THE RATE OF GENERIC GORENSTEIN K-ALGEBRAS”

Abstract. The rate of a standard graded K-algebra A is a measure of the growth of the shifts in a minimal free resolution of K as A-module. In particular A has rate one if and only if A is Koszul. It is known that a generic Artinian Gorenstein algebra of socle degree three is Koszul. We extend this result showing that if A is a generic Artinian Gorenstein algebra of socle degree s ≥ 3, then the rate of A is ⌊s/2⌋. In proving it, we get that a generic Artinian Gorenstein K-algebra of embedding dimension at least four and socle degree s ≥ 3 is generated in degree ⌊s/2⌋ + 1. This gives a partial positive answer to a longstanding conjecture stated by M. Boij on the resolution of a generic Artinian Gorenstein ring of odd socle degree. This is a joint work with M.Boij, A. De Stefani and M.E. Rossi.