The Picard index of a surface with torus action
Justus Springer
TL;DR
This paper derives a formula for the Picard index of certain algebraic surfaces with torus actions and classifies specific log del Pezzo surfaces with low Picard index.
Contribution
It introduces a formula for the Picard index of rational surfaces with torus action and classifies log del Pezzo surfaces with Picard number one up to a certain Picard index.
Findings
Derived a formula for the Picard index of surfaces with torus action.
Classified log del Pezzo surfaces with Picard number one up to Picard index 10,000.
Abstract
We consider normal rational projective surfaces with torus action and provide a formula for their Picard index, that means the index of the Picard group inside the divisor class group. As an application, we classify the log del Pezzo surfaces with torus action of Picard number one up to Picard index 10,000.
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Taxonomy
TopicsAlgebraic Geometry and Number Theory · Historical Studies and Socio-cultural Analysis · Analytic Number Theory Research