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Trigonal Canonically Fibered Surfaces
Houari Benammar Ammar, Xi Chen, Nathan Grieve
https://arxiv.org/abs/2506.01526 https://arxiv.or…

Trigonal Canonically Fibered Surfaces
We fix some gaps of a proof of Xiao's conjecture on canonically fibered surfaces of relative genus 5 by the second author. Our argument simplifies the original proof and gives a much better bound on the geometric genus of the surface. Also we apply the same argument to canonically fibered surfaces of relative genus 3 and 4 to obtain some Noether-type inequalities for these surfaces.