Description
Title: Koszul algebras V
Abstract: In the first half of the talk, we shall recall Koszul filtation
and Grobner flag. Let R be a standard graded algebra. If R has a Koszul
filtation, then R is Koszul. If R has a Grobner flag, then R is
G-quadratic. I will mention an important result of Conca, Rossi, and
Valla: Let R be a quadratic Gorenstein algebra with Hilbert series 1 + nz
+ nz^2 + n^3. Then for n=3 and n=4, R is Koszul.
In the second half of the talk, we shall focus on class of strongly Koszul
algebras. If time permits, I will prove that Koszul algebras are preserved
under various classical constructions, in particular, under taking tensor
products, Segre products, fibre products and Veronese subrings.