A145582 Number of isomorphism classes of rank one toric log del Pezzo surfaces with index L = n.

5, 7, 18, 13, 33, 26, 45, 27, 51, 51, 67, 53, 69, 74, 133, 48, 89, 81, 102, 110, 178, 105, 124, 109, 161, 119, 164, 135, 142, 187, 140, 105, 274, 159, 383, 169, 145, 166, 329, 221, 177, 266, 180, 230, 404, 189, 220, 213, 315, 264, 384, 233, 225, 260, 573, 298

Offset: 1

Author

Jonathan Vos Post, Oct 14 2008

Keywords

• nonn

Comments

A145581(n) is the number of toric log del Pezzo surfaces with index L = n. Both are in the table for Theorem 1.2, p. 4 of Kasprzyk, Kreuzer and Nill.

Links

• Justus Springer, Table of n, a(n) for n = 1..5000
• Andreas Bäuerle, Sharp volume and multiplicity bounds for Fano simplices, arXiv:2308.12719 [math.CO], 2023.
• Andreas Bäuerle, Classification of Fano simplices
• Daniel Haettig, Beatrice Hafner, Juergen Hausen and Justus Springer, Del Pezzo surfaces of Picard number one admitting a torus action, arXiv:2207.14790 [math.AG], 2022. [see Proposition 7.1, p. 27]
• Daniel Hättig, Jürgen Hausen, Justus Springer and Hendrik Süß, Log del Pezzo surfaces with torus action - a searchable database
• Alexander M. Kasprzyk, Maximilian Kreuzer and Benjamin Nill, On the combinatorial classification of toric log del Pezzo surfaces, LMS J. Comput. Math. 13 (2010) 33-46; arXiv:0810.2207 [math.AG], 2008.
• Alexander M. Kasprzyk and Benjamin Nill, Chapter 17 Fano polytopes, in: Strings, Gauge Fields, And The Geometry Behind, World Scientific, 2012. See p. 359.

Crossrefs

Cf. A145581, A364712.

Extensions

a(17) from Kasprzyk and Nill (2012) added by Andrey Zabolotskiy, Feb 17 2020

a(18)-a(200) from Haettig, Hafner, Hausen and Springer (2022) added by Justus Springer, Aug 04 2023

a(201)-a(1000) from Bäuerle's data, added by Andrey Zabolotskiy, Oct 01 2023

a(1001)-a(5000) computed using Bäuerle's algorithm, added by Justus Springer, Apr 15 2024