Marilena Crupi: Algebraic invariants of graded ideals with a given Hilbert function in an exterior algebra, p.393-403

Abstract:

Let $E=K\left\langle e_1,\ldots , e_n\right\rangle$ be the exterior algebra over an $n$-dimensional vector space $V$ with basis $e_1,\ldots,e_n$ over some field $K$. We introduce the universal lexsegment ideals in $E$ and we devote our attention to their Hilbert function. Hence, we analyze the depth and the graded Betti numbers of a graded ideal with a given Hilbert function in $E$, via such a class of monomial ideals.

Key Words: Exterior algebra, monomial ideals, lexicographic ideals, minimal resolutions, standard invariants.

2000 Mathematics Subject Classification: Primary: 13A02;
Secondary: 15A75, 18G10.

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