Rachel PriesAffiliation: Colorado State University Title Of Talk: Supersingular curves that are cyclic covers of the projective line
URLS: Abstract: The celebrated Eichler--Deuring mass formula counts the number of supersingular elliptic curves in positive characteristic. Ibukiyama, Katsura, and Oort generalized this formula to count the number of supersingular curves of genus 2 that have an automorphism of order 3 or order 4. In this talk, I will explain how to generalize these results for any 1-parameter family of cyclic covers of the projective line. This gives a formula for the number of non-ordinary curves in the family in positive characteristic. The proof uses intersection theory in the Chow ring and is joint work with Cavalieri. If time permits, I will talk about (i) in-progress work with Cavalieri and Mantovan, where we find a formula for the number of supersingular curves in special families of curves of genus 3-7; and (ii) some joint work with Booher about the existence of supersingular curves of genus 5 for all primes congruent to 3 modulo 4.
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Last update made Tue Mar 10 21:28:05 CDT 2026.
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