The $a_0$-invariants of powers of a two-dimensional squarefree monomial ideal

Abstract

Let ∆ be an one-dimensional simplicial complex on {1, 2, . . . , s} and S the polynomial ring K[x 1 , . . . , x s ] over a field K. The explicit formula for a 0 (S/I n ∆ ) is presented when girth(∆) ≥ 4. If girth(∆) = 3 we characterize the simplicial complexes ∆ for which a 0 (S/I n ∆ ) = 3n − 1 or 3n − 2.