Cyclic coverings of the projective line by Mumford curves in positive characteristic

AbstractIn this paper, we use the perspective of linear series, and in particular results following from the degeneration tools of limit linear series, to give a number of new results on the existence and non-existence of tamely branched covers of the projective line in positive characteristic. Our results are both in terms of ramification indices and the sharper invariant of monodromy cycles, and the first class of results are obtained by intrinsically algebraic and positive-characteristic arguments.

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Inverse Galois problem for ordinary curves

International Journal of Number Theory ◽

10.1142/s1793042118500811 ◽

2018 ◽

Vol 14 (05) ◽

pp. 1305-1315

Author(s):

Raymond van Bommel

Keyword(s):

Positive Characteristic ◽

Function Fields ◽

Projective Line ◽

Stable Curves ◽

Inverse Galois Problem ◽

Galois Covers

We consider the inverse Galois problem over function fields of positive characteristic [Formula: see text], for example, over the projective line. We describe a method to construct certain Galois covers of the projective line and other curves, which are ordinary in the sense that their Jacobian has maximal [Formula: see text]-torsion. We do this by constructing Galois covers of ordinary semi-stable curves, and then deforming them into smooth Galois covers.

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Hyperelliptic curves among cyclic coverings of the projective line, II

Archiv der Mathematik ◽

10.1007/s00013-014-0609-5 ◽

2014 ◽

Vol 102 (2) ◽

pp. 113-116 ◽

Cited By ~ 1

Author(s):

Nan Wangyu ◽

Fumio Sakai

Keyword(s):

Projective Line ◽

Hyperelliptic Curves ◽

Cyclic Coverings

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Cyclic coverings of the p-adic projective line by Mumford curves

manuscripta mathematica ◽

10.1007/s00229-007-0120-4 ◽

2007 ◽

Vol 124 (1) ◽

pp. 77-95 ◽

Cited By ~ 3

Author(s):

Patrick Erik Bradley

Keyword(s):

Projective Line ◽

Cyclic Coverings

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Recurrence on infinite cyclic coverings

Astérisque ◽

10.24033/ast.1105 ◽

2020 ◽

Vol 415 ◽

pp. 195-214

Author(s):

Albert FATHI

Keyword(s):

Cyclic Coverings

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Singularities of plane complex curves and limits of Kähler metrics with cone singularities. I: Tangent Cones

Complex Manifolds ◽

10.1515/coma-2017-0005 ◽

2017 ◽

Vol 4 (1) ◽

pp. 43-72 ◽

Cited By ~ 1

Author(s):

Martin de Borbon

Keyword(s):

Vector Field ◽

Einstein Metrics ◽

Projective Line ◽

Tangent Cones ◽

Reeb Vector ◽

Reeb Vector Field ◽

Complex Curves ◽

Complex Dimensions ◽

Irregular Case ◽

Kähler Einstein Metrics

Abstract The goal of this article is to provide a construction and classification, in the case of two complex dimensions, of the possible tangent cones at points of limit spaces of non-collapsed sequences of Kähler-Einstein metrics with cone singularities. The proofs and constructions are completely elementary, nevertheless they have an intrinsic beauty. In a few words; tangent cones correspond to spherical metrics with cone singularities in the projective line by means of the Kähler quotient construction with respect to the S1-action generated by the Reeb vector field, except in the irregular case ℂβ₁×ℂβ₂ with β₂/ β₁ ∉ Q.

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