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On metric graphs with prescribed gonality
- Publication Year :
- 2016
-
Abstract
- We prove that in the moduli space of genus-g metric graphs the locus of graphs with gonality at most d has the classical dimension min{3g-3,2g+2d-5}. This follows from a careful parameter count to establish the upper bound and a construction of sufficiently many graphs with gonality at most d to establish the lower bound. Here, gonality is the minimal degree of a non-degenerate harmonic map to a tree that satisfies the Riemann-Hurwitz condition everywhere. Along the way, we establish a convenient combinatorial datum capturing such harmonic maps to trees.<br />Comment: 18 pages, 10 figures, corrected an erroneous lemma in previous version, many further improvements suggested by referees
- Subjects :
- Mathematics - Combinatorics
Mathematics - Algebraic Geometry
05C99, 14T05, 14H51
Subjects
Details
- Database :
- arXiv
- Publication Type :
- Report
- Accession number :
- edsarx.1602.05542
- Document Type :
- Working Paper