Inequalities and enumerative formulas for flags of Pfaff systems
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866911320264146944 |
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| author | Peña, Miguel Rodríguez Lourenço, Fernando |
| author_facet | Peña, Miguel Rodríguez Lourenço, Fernando |
| contents | In this work, we study inequalities and enumerative formulas for flags of Pfaff systems on $\mathbb{P}^n_{\mathbb{C}}$. More specifically, we find the number of independent Pfaff systems that leave invariant a one-dimensional holomorphic foliation and deduce inequalities relating the degrees in the flags, which can be interpreted as the Poincaré problem for flags. Moreover, restricting to a flag of specific holomorphic foliations/distributions, we obtain inequalities involving the degrees. As a consequence, we prove stability results for the tangent sheaf of some rank two holomorphic foliations/distributions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_17208 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Inequalities and enumerative formulas for flags of Pfaff systems Peña, Miguel Rodríguez Lourenço, Fernando Algebraic Geometry In this work, we study inequalities and enumerative formulas for flags of Pfaff systems on $\mathbb{P}^n_{\mathbb{C}}$. More specifically, we find the number of independent Pfaff systems that leave invariant a one-dimensional holomorphic foliation and deduce inequalities relating the degrees in the flags, which can be interpreted as the Poincaré problem for flags. Moreover, restricting to a flag of specific holomorphic foliations/distributions, we obtain inequalities involving the degrees. As a consequence, we prove stability results for the tangent sheaf of some rank two holomorphic foliations/distributions. |
| title | Inequalities and enumerative formulas for flags of Pfaff systems |
| topic | Algebraic Geometry |
| url | https://arxiv.org/abs/2401.17208 |