Degenerations of maps to projective spaces
Fuente:
arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866912459625857024 |
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| author | Esteves, Eduardo Rodriguez, Piere Vital, Eduardo |
| author_facet | Esteves, Eduardo Rodriguez, Piere Vital, Eduardo |
| contents | Degenerations of linear series on smooth projective varieties approaching multicomponent varieties $X$ give rise to certain quiver representations in the category of linear series over $X$, which yield rational maps from $X$ to the corresponding quiver Grassmannians of codimension 1 subspaces. We describe these quiver Grassmannians for the case of the simplest quiver, arising when $X$ has only two components. We prove that they are reduced, local complete intersections whose components are rational of the same dimension. Also, we show that they are limits of projective spaces when they do arise from degenerations, and thus are special fibers of certain Mustafin varieties. Finally, we address a Riemann--Roch question for these quiver representations. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_00901 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Degenerations of maps to projective spaces Esteves, Eduardo Rodriguez, Piere Vital, Eduardo Algebraic Geometry Representation Theory Degenerations of linear series on smooth projective varieties approaching multicomponent varieties $X$ give rise to certain quiver representations in the category of linear series over $X$, which yield rational maps from $X$ to the corresponding quiver Grassmannians of codimension 1 subspaces. We describe these quiver Grassmannians for the case of the simplest quiver, arising when $X$ has only two components. We prove that they are reduced, local complete intersections whose components are rational of the same dimension. Also, we show that they are limits of projective spaces when they do arise from degenerations, and thus are special fibers of certain Mustafin varieties. Finally, we address a Riemann--Roch question for these quiver representations. |
| title | Degenerations of maps to projective spaces |
| topic | Algebraic Geometry Representation Theory |
| url | https://arxiv.org/abs/2507.00901 |