A simply connected numerical Godeaux surface with ample canonical class

Abstract

We prove that a recent construction of a numerical Godeaux surface due to P. Craighero and R. Gattazzo is simply connected, and show how to realize their construction as a double plane. By proving that the surface contains no (-2)-curves, we obtain that this is the first example of a simply connected surface with vanishing geometric genus and ample canonical class.

plain Tex 22 pages; 1 figure added, revised proofs of several results, corrected typos

Cited by in corpus (10)

• A simply connected surface of general type with p_g=0 and K^2=2
• Einstein metrics and smooth structures
• Bloch's conjecture for the surface of Craighero and Gattazzo
• Bloch's conjecture on surfaces of general type with an involution
• Numerical Godeaux surfaces with an involution
• Degenerations of Godeaux surfaces and exceptional vector bundles
• Involutions on algebraic surfaces and zero cycles
• Geometry of quintics in ${\mathbb{P}}^3$ and the Craighero-Gattazzo surface of general type
• Chow groups of conic bundles in ${\mathbb{P}}^5$ and the Generalised Bloch's conjecture
• Involutions on algebraic surfaces and the Generalised Bloch's conjecture