Effective algebraic integration in bounded genus
Accepted version
Peer-reviewed
Repository URI
Repository DOI
Change log
Authors
Pereira, JV
Svaldi, Roberto https://orcid.org/0000-0003-1489-5899
Abstract
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.
Description
Keywords
math.AG, math.AG, math.CA, 37F75, 14E99
Journal Title
Algebraic Geometry
Conference Name
Journal ISSN
2313-1691
2214-2584
2214-2584
Volume Title
6
Publisher
Foundation Compositio Mathematica
Publisher DOI
Sponsorship
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.