Preperiodic dynatomic curves for $z ↦ z^{d} + c$

Yan Gao

Preperiodic dynatomic curves for

z \mapsto z^{d} + c

Yan Gao

Fundamenta Mathematicae, Tome 233 (2016), p. 37-69 / Harvested from The Polish Digital Mathematics Library

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Résumé

The preperiodic dynatomic curve $_{n, p}$ is the closure in ℂ² of the set of (c,z) such that z is a preperiodic point of the polynomial $z \mapsto z^{d} + c$ with preperiod n and period p (n,p ≥ 1). We prove that each $_{n, p}$ has exactly d-1 irreducible components, which are all smooth and have pairwise transverse intersections at the singular points of $_{n, p}$ . We also compute the genus of each component and the Galois group of the defining polynomial of $_{n, p}$ .

Publié le : 2016-01-01

Zbl 06545389

EUDML-ID : urn:eudml:doc:286217

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     author = {Yan Gao},
     title = {Preperiodic dynatomic curves for $z - z^{d} + c$
            },
     journal = {Fundamenta Mathematicae},
     volume = {233},
     year = {2016},
     pages = {37-69},
     zbl = {06545389},
     language = {en},
     url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-fm91-12-2015}
}

Yan Gao. Preperiodic dynatomic curves for $z ↦ z^{d} + c$
            . Fundamenta Mathematicae, Tome 233 (2016) pp. 37-69. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-fm91-12-2015/