The Picard index of a surface with torus action

Author:

Springer Justus

Abstract

AbstractWe 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 $$ 10\,000 $$ 10 000 .

Funder

Eberhard Karls Universität Tübingen

Publisher

Springer Science and Business Media LLC

Reference21 articles.

1. Alekseev, V.A., Nikulin, V.V.: Classification of del Pezzo surfaces with log-terminal singularities of index $$\le 2$$ and involutions on $$K3$$ surfaces. Dokl. Akad. Nauk SSSR 306(3), 525-528 (1989) (Russian)

2. English transl., Soviet Math. Dokl. 39(3), 507-511 (1989)

3. Arzhantsev, I., Derenthal, U., Hausen, J., Laface, A.: Cox rings, vol. 144. Cambridge Studies in Advanced Mathematics, Cambridge University Press, Cambridge (2015)

4. Bäuerle, A.: Sharp volume and multiplicity bounds for Fano simplices, arXiv:2308.12719, primary class math.CO (2023)

5. Cox, D.A., Little, J.B., Schenck, H.K.: Toric varieties, vol. 124. Graduate Studies in Mathematics, American Mathematical Society, Providence, RI (2011)

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