Derived categories of quadric bundles and moduli stacks of spinor sheaves
Fuente:
arXiv
Salvato in:
| Autori principali: | , |
|---|---|
| Natura: | Preprint |
| Pubblicazione: |
2026
|
| Soggetti: | |
| Accesso online: | |
| Tags: |
Aggiungi Tag
Nessun Tag, puoi essere il primo ad aggiungerne!!
|
| _version_ | 1866917290467917824 |
|---|---|
| author | Cheng, Raymond Olander, Noah |
| author_facet | Cheng, Raymond Olander, Noah |
| contents | We prove that the Kuznetsov component of a flat family of even-dimensional quadrics of corank at most 2 is equivalent to the twisted derived category of an algebraic space whenever: (i) the open subset of the base over which the quadrics has corank at most 1 is scheme-theoretically dense; and (ii) a certain étale double cover of the closed complement admits a section. This provides the first general geometricity result for Kuznetsov components of higher dimensional quadrics, thereby generalizing works of Kapranov, Bondal, Orlov, Kuznetsov, Moschetti, Xie, and others. Our main tool is the moduli stack of spinor sheaves on a family of quadrics, which we define and study in detail. In the situation of our main result, we produce an open substack which is a $\mathbf{G}_m$-gerbe, and show that the associated twisted derived category is equivalent to the Kuznetsov component of the family of quadrics, thereby providing a geometric interpretation of the Brauer classes appearing in previous works. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_20263 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Derived categories of quadric bundles and moduli stacks of spinor sheaves Cheng, Raymond Olander, Noah Algebraic Geometry 14F08, 14D23 (primary), 14F22, 14D10 (secondary) We prove that the Kuznetsov component of a flat family of even-dimensional quadrics of corank at most 2 is equivalent to the twisted derived category of an algebraic space whenever: (i) the open subset of the base over which the quadrics has corank at most 1 is scheme-theoretically dense; and (ii) a certain étale double cover of the closed complement admits a section. This provides the first general geometricity result for Kuznetsov components of higher dimensional quadrics, thereby generalizing works of Kapranov, Bondal, Orlov, Kuznetsov, Moschetti, Xie, and others. Our main tool is the moduli stack of spinor sheaves on a family of quadrics, which we define and study in detail. In the situation of our main result, we produce an open substack which is a $\mathbf{G}_m$-gerbe, and show that the associated twisted derived category is equivalent to the Kuznetsov component of the family of quadrics, thereby providing a geometric interpretation of the Brauer classes appearing in previous works. |
| title | Derived categories of quadric bundles and moduli stacks of spinor sheaves |
| topic | Algebraic Geometry 14F08, 14D23 (primary), 14F22, 14D10 (secondary) |
| url | https://arxiv.org/abs/2602.20263 |