Stable reduction of three-point covers
FakultätenFakultät für Mathematik und Wirtschaftswissenschaften
Let R be a complete discrete valuation ring with fraction field K and residue field k. We assume that the characteristic of K is 0 and the characteristic of k is p>0. Additionally, we assume that k is algebraically closed. Further, we assume that all curves are absolutely irreducible, smooth and projective. In this thesis we study the stable reduction of a certain class of three-point covers which are defined over K. These three-point covers are defined as the Galois closure of three-point covers between genus-0 curves, which are defined over K, and which are ramified and branched in exactly three distinct points.The main result in this thesis is the complete description of the stable reduction in the case that the cover between genus-0 curves has degree d<2p. An important part of this description is the analysis of the so-called tail covers that occur in the stable reduction. We generalize the occurring tail covers from the case d<2p to general d and prove that these generalized tail covers also occur in the stable reduction of certain three-point covers.
Erstellung / Fertigstellung
Normierte SchlagwörterReduktionsverfahren [GND]
Arithmetical algebraic geometry [LCSH]
Geometry, algebraic [LCSH]