Paracanonical base locus, Albanese morphism, and semi-orthogonal indecomposability of derived categories
Fuente:
arXiv
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| Formato: | Preprint |
| Publicado: |
2021
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| _version_ | 1866914991167242240 |
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| author | Caucci, Federico |
| author_facet | Caucci, Federico |
| contents | Motivated by an indecomposability criterion of Xun Lin for the bounded derived category of coherent sheaves on a smooth projective variety $X$, we study the paracanonical base locus of $X$, that is the intersection of the base loci of $ω_X \otimes P_α$, for all $α\in \mathrm{Pic}^0 X$. We prove that this is equal to the relative base locus of $ω_X$ with respect to the Albanese morphism of $X$. As an application, we get that bounded derived categories of Hilbert schemes of points on certain surfaces do not admit non-trivial semi-orthogonal decompositions. We also have a consequence on the indecomposability of bounded derived categories in families. Finally, our viewpoint allows to unify and extend some results recently appearing in the literature. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2110_06795 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | Paracanonical base locus, Albanese morphism, and semi-orthogonal indecomposability of derived categories Caucci, Federico Algebraic Geometry Motivated by an indecomposability criterion of Xun Lin for the bounded derived category of coherent sheaves on a smooth projective variety $X$, we study the paracanonical base locus of $X$, that is the intersection of the base loci of $ω_X \otimes P_α$, for all $α\in \mathrm{Pic}^0 X$. We prove that this is equal to the relative base locus of $ω_X$ with respect to the Albanese morphism of $X$. As an application, we get that bounded derived categories of Hilbert schemes of points on certain surfaces do not admit non-trivial semi-orthogonal decompositions. We also have a consequence on the indecomposability of bounded derived categories in families. Finally, our viewpoint allows to unify and extend some results recently appearing in the literature. |
| title | Paracanonical base locus, Albanese morphism, and semi-orthogonal indecomposability of derived categories |
| topic | Algebraic Geometry |
| url | https://arxiv.org/abs/2110.06795 |