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

1,1

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.

Sequence in context: A248480 A243844 A271656 * A034762 A138919 A345909

Adjacent sequences: A145579 A145580 A145581 * A145583 A145584 A145585

Keyword

nonn

Author

Jonathan Vos Post, Oct 14 2008

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

Status

approved