Flips for spaces of quadrics on del Pezzo varieties
Fuente:
arXiv
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| Formato: | Preprint |
| Publicado: |
2026
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| _version_ | 1866915820899139584 |
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| author | Shah, Saket |
| author_facet | Shah, Saket |
| contents | For a cubic hypersurface $X$, work of Galkin--Shinder and Voisin shows the existence of a birational map relating the Hilbert scheme of two points $X^{[2]}$ with a certain projective bundle over $X$. Belmans--Fu--Raedschelders show that this is a standard flip, a particularly nice type of birational map inducing decompositions of derived categories. We show that this geometric construction extends to produce standard flips for Hilbert schemes of quadrics on various higher-dimensional del Pezzo varieties of degree at least 3, including cubics, intersections of two quadrics, and linear sections of $\mathrm{Gr}(2, 5)$. The resulting construction also generalizes results of Chung--Hong--Lee for quintic del Pezzo varieties. As an application, we produce a conjectural semiorthogonal decompositions for orthogonal Grassmannians of lines. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_07366 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Flips for spaces of quadrics on del Pezzo varieties Shah, Saket Algebraic Geometry 14E05 (Primary), 14F08 (Secondary) For a cubic hypersurface $X$, work of Galkin--Shinder and Voisin shows the existence of a birational map relating the Hilbert scheme of two points $X^{[2]}$ with a certain projective bundle over $X$. Belmans--Fu--Raedschelders show that this is a standard flip, a particularly nice type of birational map inducing decompositions of derived categories. We show that this geometric construction extends to produce standard flips for Hilbert schemes of quadrics on various higher-dimensional del Pezzo varieties of degree at least 3, including cubics, intersections of two quadrics, and linear sections of $\mathrm{Gr}(2, 5)$. The resulting construction also generalizes results of Chung--Hong--Lee for quintic del Pezzo varieties. As an application, we produce a conjectural semiorthogonal decompositions for orthogonal Grassmannians of lines. |
| title | Flips for spaces of quadrics on del Pezzo varieties |
| topic | Algebraic Geometry 14E05 (Primary), 14F08 (Secondary) |
| url | https://arxiv.org/abs/2602.07366 |