Abstract
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 .
Citation
Giancarlo Urzúa. José Ignacio Yáñez. "Characterization of Kollár surfaces." Algebra Number Theory 12 (5) 1073 - 1105, 2018. https://doi.org/10.2140/ant.2018.12.1073
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