// Workers AI · dad joke modeWhat did the Horikawa surface say? I'm a curve above the rest.

In mathematics, a Horikawa surface is one of the surfaces of general type introduced by Eiji Horikawa.

These are surfaces with q = 0 and p_g = c₁²/2 + 2 or c₁²/2 + 3/2 (which implies that they are more or less on the Noether line edge of the region of possible values of the Chern numbers).

They are all simply connected, and Horikawa gave a detailed description of them.

References

• Barth, Wolf P.; Hulek, Klaus; Peters, Chris A.M.; Van de Ven, Antonius (2004). Compact Complex Surfaces. Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge. Vol. 4. Springer-Verlag, Berlin. ISBN 978-3-540-00832-3. MR 2030225.