  The purpose of this note is to suggest an analogue for genus 2 curves of part
of Gross and Zagier's work on elliptic curves. Experimentally, for genus 2
curves with CM by a quartic CM field K, it appears that primes dividing the
denominators of the discriminants of the Igusa class polynomials all have the
property 1) that they are bounded by d, the absolute value of the discriminant
of K, and 2) that they divide d-x^2, for some integer x whose square is less
than d. A slightly stronger condition is given in Section 3. Such primes are
primes of bad reduction for the genus 2 curve and primes of supersingular
reduction for the Jacobian of the genus 2 curve.
