Abstract
If a curve X of genus g is a double covering of a curve C of genus h such that g ≥ 6h−3 ≥ 9, there is an explicit relation between the gonality sequences of X and C. In particular, it shows that X violates the slope inequalities if and only if C does. This provides new examples of curves X violating the slope inequalities.
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References
Accola R.D.M.: Riemann surfaces with automorphism groups admitting partitions. Proc. AMS 21, 477–482 (1969)
E. Arbarello et al., Geometry of Algebraic Curves. I, Grundlehren Math. Wiss., vol. 267. Springer, New York 1985
T. Harui, Projective models of double coverings of hyperelliptic curves, Preprint 2014
Harui T., Kato T., Ohbuchi A.: The minimal degree of plane models of algebraic curves and double coverings. Geom. Dedicata 143, 181–192 (2009)
T. Kato and G. Martens, Algebraic curves violating the slope inequalities, Preprint 2013
Lange H., Martens G.: On the gonality sequence of an algebraic curve. manuscr. math. 137, 457–473 (2012)
H. Lange and P.E. Newstead, Clifford indices for vector bundles on curves, In: A. Schmitt (ed): Affine flag manifolds and principal bundles, 165–202, Trends Math. Birkhaeuser/Springer 2010
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Kato, T., Martens, G. The gonality sequence of a curve with an involution. Arch. Math. 103, 111–116 (2014). https://doi.org/10.1007/s00013-014-0668-7
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DOI: https://doi.org/10.1007/s00013-014-0668-7