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Real trigonal curves and real elliptic surfaces of type I
-
Alex Degtyarev
,
Ilia Itenberg
Published/Copyright:
March 31, 2012
Abstract.
We study real trigonal curves and elliptic surfaces of type I (over a base of an arbitrary genus) and their fiberwise equivariant deformations. The principal tool is a real version of Grothendieck's dessins d'enfants. We give a description of maximally inflected trigonal curves of type I in terms of the combinatorics of sufficiently simple graphs and, in the case of the rational base, obtain a complete classification of such curves. As a consequence, these results lead to conclusions concerning real Jacobian elliptic surfaces of type I with all singular fibers real.
Received: 2012-01-06
Published Online: 2012-03-31
Published in Print: 2014-01-01
© 2014 by Walter de Gruyter Berlin Boston
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Articles in the same Issue
- Masthead
- Constant mean curvature surfaces in hyperbolic 3-space via loop groups
- La formule des traces pour les revêtements de groupes réductifs connexes. I. Le développement géométrique fin
- Heegner cycles and derivatives of p-adic L-functions
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- Stability of the positive mass theorem for rotationally symmetric Riemannian manifolds
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