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| Auteurs principaux: | , , , |
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| Format: | Preprint |
| Publié: |
2026
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| Sujets: | |
| Accès en ligne: | https://arxiv.org/abs/2604.21242 |
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| _version_ | 1866910159122464768 |
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| author | Bertram, Aaron Fleck, Jonathon Pan, Liebo Sullivan, Joseph |
| author_facet | Bertram, Aaron Fleck, Jonathon Pan, Liebo Sullivan, Joseph |
| contents | Reider's Theorem on the very ampleness of adjoint linear series on a complex projective algebraic surface is extended in two new directions. First, Reider-type inequalities are shown to imply nefness of linear series of the form dH - E on the blow-up of projective space along the embedded surface. This can be thought of as a weak analogy of Saint-Donat's Theorem on the generators of the ideal of a curve embedded by an adjoint linear series. Next, Reider-type inequalities give a sharp estimate for the ample cone of the Hilbert schemes of length d subschemes of the surface. The proofs consist of (a) finding a natural family of objects parametrized by the base (either the blow-up along the surface or the Hilbert scheme) and (b) finding the largest chamber in the stability manifold of the surface where the objects in the family are all Bridgeland semistable. A Theorem of Bayer-Macri then gives nefness of the determinant line bundle on the base of the family. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_21242 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Two New Extensions of Reider's Theorem on Algebraic Surfaces Bertram, Aaron Fleck, Jonathon Pan, Liebo Sullivan, Joseph Algebraic Geometry Reider's Theorem on the very ampleness of adjoint linear series on a complex projective algebraic surface is extended in two new directions. First, Reider-type inequalities are shown to imply nefness of linear series of the form dH - E on the blow-up of projective space along the embedded surface. This can be thought of as a weak analogy of Saint-Donat's Theorem on the generators of the ideal of a curve embedded by an adjoint linear series. Next, Reider-type inequalities give a sharp estimate for the ample cone of the Hilbert schemes of length d subschemes of the surface. The proofs consist of (a) finding a natural family of objects parametrized by the base (either the blow-up along the surface or the Hilbert scheme) and (b) finding the largest chamber in the stability manifold of the surface where the objects in the family are all Bridgeland semistable. A Theorem of Bayer-Macri then gives nefness of the determinant line bundle on the base of the family. |
| title | Two New Extensions of Reider's Theorem on Algebraic Surfaces |
| topic | Algebraic Geometry |
| url | https://arxiv.org/abs/2604.21242 |