1. Alternating Catalan numbers and curves with triple ramification
- Author
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Gian Pietro Pirola, Juan Carlos Naranjo, Riccardo Moschetti, and Gavril Farkas
- Subjects
Degree (graph theory) ,Algebraic curves ,Ramification (botany) ,Teoria de grups ,Combinatòria (Matemàtica) ,Group Theory (math.GR) ,Theoretical Computer Science ,Algebraic geometry ,Combinatorics ,Catalan number ,Mathematics - Algebraic Geometry ,Mathematics::Algebraic Geometry ,Geometria algebraica ,Mathematics (miscellaneous) ,FOS: Mathematics ,Mathematics - Combinatorics ,Computer Science::General Literature ,Combinations ,Combinatorics (math.CO) ,Corbes algebraiques ,Group theory ,Mathematics - Group Theory ,Algebraic Geometry (math.AG) ,Mathematics - Abstract
It is known that the monodromy group of each cover of a general curve of genus g>3 equals either the symmetric or the alternating group. The classical Catalan numbers count the minimal degree covers (with symmetric monodromy) of a general curve of even genus. We solve the analogous problem for the alternating group and we determine the number of alternating covers of minimal degree 2g+1 of a general curve of genus g., 18 pages. Minor improvements, also referencing the related work of Lian. Final version to appear in Annali Scuola Normale di Pisa
- Published
- 2021
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