Xiao's conjecture for canonically fibered surfaces of relative genus 5 is proved: nonhyperelliptic examples have rational base and geometric genus at most 50, and combining with the hyperelliptic case gives pg at most 52.
The minimal number of quotient singularities on surfaces with given numerical invariants
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Trigonal Canonically Fibered Surfaces
Xiao's conjecture for canonically fibered surfaces of relative genus 5 is proved: nonhyperelliptic examples have rational base and geometric genus at most 50, and combining with the hyperelliptic case gives pg at most 52.