Singularities of multiplicative $p$-closed vector fields and global 1-forms of Zariski surfaces

Hirokado, Masayuki

J. Math. Kyoto Univ., Tome 39 (1999) no. 4, p. 455-468 / Harvested from Project Euclid

Résumé

We consider quotient surfaces by $p$-closed rational vector fields. First we show that singularities on the quotient surfaces by multiplicative $p$-closed vector fields are tonic singularities. Then we proceed to studying global properties of Zariski surfaces. We see that non-trivial global 1-forms are related to some linear systems with base points. We also give examples of Zariski surfaces admitting non-closed regular 1-forms.

Publié le : 1999-05-15
Classification: 14J17, 14F10, 14J28

@article{1250517864,
     author = {Hirokado, Masayuki},
     title = {Singularities of multiplicative $p$-closed vector fields and global 1-forms of Zariski surfaces},
     journal = {J. Math. Kyoto Univ.},
     volume = {39},
     number = {4},
     year = {1999},
     pages = { 455-468},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1250517864}
}

Hirokado, Masayuki. Singularities of multiplicative $p$-closed vector fields and global 1-forms of Zariski surfaces. J. Math. Kyoto Univ., Tome 39 (1999) no. 4, pp.  455-468. http://gdmltest.u-ga.fr/item/1250517864/