Primes Dividing Invariants of CM Picard Curves

Pınar Kılıçer, Elisa Lorenzo García, Marco Streng

Research output: Contribution to journalArticleAcademicpeer-review

4 Citations (Scopus)
28 Downloads (Pure)


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.
Original languageEnglish
Pages (from-to)480-504
Number of pages25
JournalCanadian journal of mathematics-Journal canadien de mathematiques
Issue number2
Early online date15-Nov-2018
Publication statusPublished - Apr-2020


  • math.NT
  • math.AG
  • 14H45, 14K22, 11H06, 14G50, 14H40, 14Q05

Cite this