Mapping cones of monomial ideals over exterior algebras
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arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2023
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| _version_ | 1866909198615314432 |
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| author | Crupi, Marilena Ficarra, Antonino Lax, Ernesto |
| author_facet | Crupi, Marilena Ficarra, Antonino Lax, Ernesto |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2303_06953 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Mapping cones of monomial ideals over exterior algebras Crupi, Marilena Ficarra, Antonino Lax, Ernesto Commutative Algebra 13D02, 13C13, 15A75 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. |
| title | Mapping cones of monomial ideals over exterior algebras |
| topic | Commutative Algebra 13D02, 13C13, 15A75 |
| url | https://arxiv.org/abs/2303.06953 |