Rank $2$ aCM and Ulrich bundles on Fano and Calabi--Yau double coverings of $\mathbb{P}^3$
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866909878729048064 |
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| author | Vacca, Roberto |
| author_facet | Vacca, Roberto |
| contents | We prove existence of aCM and Ulrich sheaves respect to ample and globally generated polarisations on a class of special finite coverings $f:X\to\mathbb{P}^n$, which in particular contains cyclic ones. In the case of rank $2$ on double coverings, we have a precise description of the zero loci of such sheaves which allows us to study their geometry and classify all possible such bundles in the case $X$ is regular. We show that on a general double covering of $\mathbb{P}^3$ branched along a divisor of degree $4,6,8$ all the above sheaves exist and, when stable, we compute the dimension of their component in the moduli spaces. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_26850 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Rank $2$ aCM and Ulrich bundles on Fano and Calabi--Yau double coverings of $\mathbb{P}^3$ Vacca, Roberto Algebraic Geometry We prove existence of aCM and Ulrich sheaves respect to ample and globally generated polarisations on a class of special finite coverings $f:X\to\mathbb{P}^n$, which in particular contains cyclic ones. In the case of rank $2$ on double coverings, we have a precise description of the zero loci of such sheaves which allows us to study their geometry and classify all possible such bundles in the case $X$ is regular. We show that on a general double covering of $\mathbb{P}^3$ branched along a divisor of degree $4,6,8$ all the above sheaves exist and, when stable, we compute the dimension of their component in the moduli spaces. |
| title | Rank $2$ aCM and Ulrich bundles on Fano and Calabi--Yau double coverings of $\mathbb{P}^3$ |
| topic | Algebraic Geometry |
| url | https://arxiv.org/abs/2510.26850 |