Effective algebraic integration in bounded genus
| Autor: | Jorge Vitório Pereira, Roberto Svaldi |
|---|---|
| Přispěvatelé: | Svaldi, Roberto [0000-0003-1489-5899], Apollo - University of Cambridge Repository |
| Rok vydání: | 2016 |
| Předmět: |
Mathematics::Dynamical Systems
Library science 01 natural sciences Computer Science::Digital Libraries 37F75 14E99 Mathematics - Algebraic Geometry math.AG Mathematics::Algebraic Geometry Genus (mathematics) Political science 0103 physical sciences Classical Analysis and ODEs (math.CA) FOS: Mathematics media_common.cataloged_instance 0101 mathematics European union Algebraic number QA Mathematics::Symplectic Geometry Algebraic Geometry (math.AG) media_common Algebra and Number Theory 010102 general mathematics math.CA Work (electrical) Mathematics - Classical Analysis and ODEs Bounded function 010307 mathematical physics Geometry and Topology Mathematics::Differential Geometry |
| ISSN: | 2214-2584 |
| Popis: | We introduce and study birational invariants for foliations on projective surfaces built from the adjoint linear series of positive powers of the canonical bundle of the foliation. We apply the results in order to investigate the effective algebraic integration of foliations on the projective plane. In particular, we describe the Zariski closure of the set of foliations on the projective plane of degree d admitting rational first integrals with fibers having geometric genus bounded by g. This collaboration initiated while both authors where visiting James McKernan at UCSD, and continued during a visit of the second author to IMPA. We are grateful to both institutions for the favorable working conditions. The first author is partially supported by Cnpq and FAPERJ. The second author was partially supported by NSF research grant no: 1200656 and no: 1265263. During the final revision of this work he was supported by funding from the European Union's Seventh Framework Programme (FP7/2007-2013)/ERC Grant agreement no. 307119. |
| Databáze: | OpenAIRE |
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