In mathematics, a Horikawa surface is one of the

surfaces of general type In algebraic geometry, a surface of general type is an algebraic surface with Kodaira dimension 2. Because of Algebraic geometry and analytic geometry#Chow.27s theorem, Chow's theorem any compact complex manifold of dimension 2 and with Kodaira ...

introduced by Horikawa. These are surfaces with ''q'' = 0 and ''p_g'' = ''c''₁²/2 + 2 or ''c''₁²/2 + 3/2 (which implies that they are more or less on the Noether line edge of the region of possible values of the

Chern number In mathematics, in particular in algebraic topology, differential geometry and algebraic geometry, the Chern classes are characteristic classes associated with complex vector bundles. They have since found applications in physics, Calabi–Yau m ...

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

References

*{{Cite book , last1=Barth , first1=Wolf P. , last2=Hulek , first2=Klaus , last3=Peters , first3=Chris A.M. , last4=Van de Ven , first4=Antonius , title=Compact Complex Surfaces , publisher= Springer-Verlag, Berlin , series=Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge. , isbn=978-3-540-00832-3 , mr=2030225 , year=2004 , volume=4 Algebraic surfaces Complex surfaces