Moduli spaces of semistable rank-2 co-Higgs bundles over P1×P1
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Bibliographic record
Abstract
It has been observed, by Rayan, that the complex projective surfaces that potentially admit non-trivial examples of semistable co-Higgs bundles must be found at the lower end of the Enriques–Kodaira classification. Motivated by this remark, it is natural to study the geometry of these objects over P1×P1. In this paper, we present necessary and sufficient conditions on the Chern classes c1,c2 of a bundle that guarantee the non-emptiness of the moduli space Mco(c1,c2) of rank 2 semistable co-Higgs bundles over P1×P1 (we do this with respect to the standard polarization). We also give an explicit description of the moduli spaces for certain choices of c1 and c2.
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Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.003 | 0.001 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.001 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.000 | 0.000 |
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