Gaeta resolutions and strange duality over rational surfaces
| Autor: | Goller, Thomas, Lin, Yinbang |
|---|---|
| Rok vydání: | 2022 |
| Předmět: | |
| Druh dokumentu: | Working Paper |
| Popis: | Over the projective plane and at most two-step blowups of Hirzebruch surfaces, where there are strong full exceptional sequences of line bundles, we obtain foundational results about Gaeta resolutions of coherent sheaves by these line bundles. Under appropriate conditions, we show the locus of semistable sheaves not admitting Gaeta resolutions has codimension at least 2. We then study Le Potier's strange duality conjecture. Over these surfaces, for two orthogonal numerical classes where one has rank one and the other has sufficiently positive first Chern class, we show that the strange morphism is injective. The main step in the proof is to use Gaeta resolutions to show that certain relevant Quot schemes are finite and reduced, allowing them to be enumerated using the authors' previous paper. Comment: 49 pages, 2 figures. We include a new result about the codimension of the locus of semistable sheaves not admitting Gaeta resolutions. We make an update because G\"ottsche and Mellit have completed the proof of the conjecture of Johnson in their recent preprint. We also use this opportunity to simplify our exposition on exceptional sequences |
| Databáze: | arXiv |
| Externí odkaz: |
|