Finite order symplectic birational self-maps on Kummer-type manifolds
Fuente:
arXiv
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| Autori principali: | , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866913103875145728 |
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| author | Dutta, Yajnaseni Mattei, Dominique Muller, Stevell Nuer, Howard |
| author_facet | Dutta, Yajnaseni Mattei, Dominique Muller, Stevell Nuer, Howard |
| contents | A projective hyperkähler manifold of Kummer-type is said to be twisted modular if it is birational to the Albanese fiber of a moduli space of twisted sheaves on an abelian surface. We prove that, with the exception of certain cases of Picard rank 3, any projective Kummer-type manifold admitting a finite-order symplectic birational self-map that acts nontrivially on its second cohomology group is twisted modular. We provide a complete characterization of these exceptions in terms of their Néron-Severi lattices. We then investigate symplectic birational self-maps of modular Kummer-type manifolds, determining exactly which Mukai vectors allow the birational transformation induced by crossing the vertical wall, which acts on cohomology as a reflection, to correspond to a finite-order symplectic birational self-map. Additionally, we prove in an appendix several results concerning moduli spaces of twisted sheaves on abelian surfaces which were not readily available in the literature. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_08062 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Finite order symplectic birational self-maps on Kummer-type manifolds Dutta, Yajnaseni Mattei, Dominique Muller, Stevell Nuer, Howard Algebraic Geometry 14J50, 14E05, 14J42, 14D20 A projective hyperkähler manifold of Kummer-type is said to be twisted modular if it is birational to the Albanese fiber of a moduli space of twisted sheaves on an abelian surface. We prove that, with the exception of certain cases of Picard rank 3, any projective Kummer-type manifold admitting a finite-order symplectic birational self-map that acts nontrivially on its second cohomology group is twisted modular. We provide a complete characterization of these exceptions in terms of their Néron-Severi lattices. We then investigate symplectic birational self-maps of modular Kummer-type manifolds, determining exactly which Mukai vectors allow the birational transformation induced by crossing the vertical wall, which acts on cohomology as a reflection, to correspond to a finite-order symplectic birational self-map. Additionally, we prove in an appendix several results concerning moduli spaces of twisted sheaves on abelian surfaces which were not readily available in the literature. |
| title | Finite order symplectic birational self-maps on Kummer-type manifolds |
| topic | Algebraic Geometry 14J50, 14E05, 14J42, 14D20 |
| url | https://arxiv.org/abs/2605.08062 |