A surface of general type with \( p_g =q =0, K² =1 \)

1994/08/24 by Caryn Werner, Werner, Caryn
Mathematics · #Algebraic Geometry and Number Theory #Geometric Analysis and Curvature Flows #Geometric and Algebraic Topology

paper · pdf · doi:10.48550/arxiv.alg-geom/9408007

Abstract

We construct a surface of general type with invariants \( χ= K² = 1 \) and torsion group \( ℤ/2 \). We use a double plane construction by finding a plane curve with certain singularities, resolving these, and taking the double cover branched along the resulting smooth curve.

Related

• A complex surface of general type with p_g=0, K²=2 and H₁=Z/2Z, Z/3Z
• A complex surface of general type with p_g=0, K²=3 and H₁=Z/2Z
• Surfaces of general type with p_g=1 and q=0
• A surface of general type with p_g=0 and K²=8 whose universal cover is not the bidisc
• Surfaces of general type with geometric genus zero: a survey