Some Results on Castelnuovo-Mumford Regularity of the Fiber Cone

On the Gorenstein property of the fiber cone to filtration

“…Since G(F) and F (F) are Cohen-Macaulay rings, these sequences are also regular sequences (the argument is similar to [P,Theorem 8]). Then for any i such that 1 [LP,Lemma 4.5]). By [BH,Proposition 3.1.19], the result follows.…”

“…Proof. For the first part we use [LP,Theorem 4.6]. For the second part is enough observe [HZ,Proposition 3.6] for the first equality and the Proposition 3.9 for the second equality.…”