Algebra & Number Theory
- Algebra Number Theory
- Volume 12, Number 5 (2018), 1073-1105.
Characterization of Kollár surfaces
Kollár (2008) introduced the surfaces
where , , and . The aim was to give many interesting examples of -homology projective planes. They occur when . For that case, we prove that Kollár surfaces are Hwang–Keum (2012) surfaces. For , we construct a geometrically explicit birational map between Kollár surfaces and cyclic covers , where are four general lines in . In addition, by using various properties on classical Dedekind sums, we prove that:
- For any , we have if and only if the Kollár surface is rational. This happens when or for some .
- For any , we have if and only if the Kollár surface is birational to a K3 surface. We classify this situation.
- For , we have that the smooth minimal model of a generic Kollár surface is of general type with .
Algebra Number Theory, Volume 12, Number 5 (2018), 1073-1105.
Received: 23 December 2016
Revised: 29 January 2018
Accepted: 17 March 2018
First available in Project Euclid: 14 August 2018
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 14J10: Families, moduli, classification: algebraic theory
Urzúa, Giancarlo; Yáñez, José Ignacio. Characterization of Kollár surfaces. Algebra Number Theory 12 (2018), no. 5, 1073--1105. doi:10.2140/ant.2018.12.1073. https://projecteuclid.org/euclid.ant/1534212097