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Primes dividing invariants of CM Picard curves. (English) Zbl 07184219
Summary: We give a bound on the primes dividing the denominators of invariants of Picard curves of genus 3 with complex multiplication. Unlike earlier bounds in genus 2 and 3, our bound is based, not on bad reduction of curves, but on a very explicit type of good reduction. This approach simultaneously yields a simplification of the proof and much sharper bounds. In fact, unlike all previous bounds for genus 3, our bound is sharp enough for use in explicit constructions of Picard curves.

##### MSC:
 14H45 Special algebraic curves and curves of low genus 14K22 Complex multiplication and abelian varieties 11H06 Lattices and convex bodies (number-theoretic aspects) 14G50 Applications to coding theory and cryptography of arithmetic geometry 14H40 Jacobians, Prym varieties 14Q05 Computational aspects of algebraic curves
genus3; SageMath
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##### References:
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