Effective algebraic integration in bounded genus

IF 1.7 1区 数学 Q1 MATHEMATICS
J. Pereira, R. Svaldi
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引用次数: 13

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.
有界属的有效代数积分
我们引入并研究了投影曲面上的叶形的双不变量,这些叶形是由叶形正则束的正幂的伴随线性级数建立的。我们应用这些结果来研究叶在投影平面上的有效代数积分。特别地,我们描述了d次投影平面上的叶形集的Zariski闭包,该叶形集允许具有几何格以g为界的纤维的有理第一积分。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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来源期刊
Algebraic Geometry
Algebraic Geometry Mathematics-Geometry and Topology
CiteScore
2.40
自引率
0.00%
发文量
25
审稿时长
52 weeks
期刊介绍: This journal is an open access journal owned by the Foundation Compositio Mathematica. The purpose of the journal is to publish first-class research papers in algebraic geometry and related fields. All contributions are required to meet high standards of quality and originality and are carefully screened by experts in the field.
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