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- W3101014835 abstract "We prove that a singular complex surface that admits a complete holomorphic vector field that has no invariant curve through a singular point of the surface is obtained from a Kato surface by contracting some divisor (in particular, it is compact). We also prove that, in a singular Stein surface endowed with a complete holomorphic vector field, a singular point of the surface where the zeros of the vector field do not accumulate is either a quasihomogeneous or a cyclic quotient singularity. We give new proofs of some results concerning the classification of compact complex surfaces admitting holomorphic vector fields. Our proofs rely in a combinatorial description of the vector field on a resolution of the singular point based on previous work of Rebelo and the author." @default.
- W3101014835 created "2020-11-23" @default.
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- W3101014835 date "2014-01-01" @default.
- W3101014835 modified "2023-09-25" @default.
- W3101014835 title "Vector fields, separatrices and Kato surfaces" @default.
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- W3101014835 doi "https://doi.org/10.5802/aif.2882" @default.
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