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arXiv · 2303.06953

Mapping cones of monomial ideals over exterior algebras

Marilena Crupi·Antonino Ficarra·Ernesto Lax
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Abstract

Let $K$ be a field, $V$ a finite dimensional $K$-vector space and $E$ the exterior algebra of $V$. We analyze iterated mapping cone over $E$. If $I$ is a monomial ideal of $E$ with linear quotients, we show that the mapping cone construction yields a minimal graded free resolution $F$ of $I$ via the Cartan complex. Moreover, we provide an explicit description of the differentials in $F$ when the ideal $I$ has a regular decomposition function. Finally, we get a formula for the graded Betti numbers of a new class of monomial ideals including the class of strongly stable ideals.

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Marilena Crupi, Antonino Ficarra, Ernesto Lax. 2023-03-13. Mapping cones of monomial ideals over exterior algebras. https://doi.org/10.1080/00927872.2023.2278665

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