Pullback and direct image of parabolic Higgs bundles and parabolic connections with symplectic and orthogonal structures
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arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866914142650105856 |
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| author | Alfaya, David Biswas, Indranil Machu, Francois-Xavier |
| author_facet | Alfaya, David Biswas, Indranil Machu, Francois-Xavier |
| contents | Given a symplectic (respectively, orthogonal) parabolic vector bundle over a compact Riemann surface, we prove that its pullback and direct image through a map between compact Riemann surfaces inherit a natural symplectic (respectively, orthogonal) structure. If the parabolic bundle is endowed with a parabolic Higgs field or a parabolic connection which are compatible with the symplectic (respectively, orthogonal) structure, then its pullback and direct image are also compatible with the resulting symplectic (respectively, orthogonal) structure. We also show that these constructions are preserved through the Nonabelian Hodge Correspondence. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_05387 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Pullback and direct image of parabolic Higgs bundles and parabolic connections with symplectic and orthogonal structures Alfaya, David Biswas, Indranil Machu, Francois-Xavier Algebraic Geometry Given a symplectic (respectively, orthogonal) parabolic vector bundle over a compact Riemann surface, we prove that its pullback and direct image through a map between compact Riemann surfaces inherit a natural symplectic (respectively, orthogonal) structure. If the parabolic bundle is endowed with a parabolic Higgs field or a parabolic connection which are compatible with the symplectic (respectively, orthogonal) structure, then its pullback and direct image are also compatible with the resulting symplectic (respectively, orthogonal) structure. We also show that these constructions are preserved through the Nonabelian Hodge Correspondence. |
| title | Pullback and direct image of parabolic Higgs bundles and parabolic connections with symplectic and orthogonal structures |
| topic | Algebraic Geometry |
| url | https://arxiv.org/abs/2511.05387 |