Green-Lazarsfeld property $N_p$ for Segre product of Hibi rings

Abstract

In this article, we prove that if a Hibi ring satisfies property $N_2$, then its Segre product with a polynomial ring in finitely many variables also satisfies property $N_2$. When the polynomial ring is in two variables, we also prove the above statement for $N_3$. Moreover, we study the minimal Koszul relations of the second syzygy module of Hibi rings.

15 pages. The previous version "Green-Lazarsfeld property $N_p$ for Hibi rings" (arXiv:2108.03915v1) has been divided into two parts. This version describes the Green-Lazarsfeld property $N_p$ for Segre product of Hibi rings. arXiv admin note: text overlap with arXiv:2108.03915