Quadratic Gorenstein Rings and the Koszul Property II

Abstract Conca–Rossi–Valla [6] ask if every quadratic Gorenstein ring $R$ of regularity three is Koszul. In [15], we use idealization to answer their question, proving that in nine or more variables there exist rings three, which are not this paper, study the analog question when four more. Let be a having ${\operatorname {codim}} \ R = c$ and {reg}} r \ge 4$. We prove $c r+1$ then always Koszul, for \geq r+2$, construct answering questions Matsuda [16] Migliore–Nagel [19].