A145582 -id:A145582 - cp's OEIS frontend

A145581 Number of isomorphism classes of toric log del Pezzo surfaces with index L = n.

16, 30, 99, 91, 250, 379, 429, 307, 690, 916, 939, 1279, 1142, 1545, 4312, 1030, 1892, 3491, 2300, 4427, 6792, 3066, 3345, 4914, 4838, 4122, 5302, 7878, 4913, 24348, 5275, 3777

Offset: 1

Jonathan Vos Post, Oct 14 2008

nonn

A145582(n) is the number of rank one 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.

Dimitrios I. Dais, On the Twelve-Point Theorem for l-Reflexive Polygons, arXiv:1806.08351 [math.CO], 2018.
Alexander M. Kasprzyk, Maximilian Kreuzer and Benjamin Nill, On the combinatorial classification of toric log del Pezzo surfaces, arXiv:0810.2207 [math.AG], 2008.
Justus Springer, RationalPolygons.jl (Version 1.1.0), implementation of algorithm by Kasprzyk, Kreuzer, and Nill, 2024.

Cf. A145582.

a(17) from Danny Rorabaugh, Jun 22 2018

a(18)-a(32) from Justus Springer, Dec 31 2024

A364712 Number of families of non-toric log del Pezzo surfaces of Picard number one with Gorenstein index = n that admit an effective action of a one-dimensional torus.

Original entry on oeis.org

13, 10, 36, 25, 80, 37, 100, 56, 109, 71, 176, 85, 158, 105, 200, 102, 226, 102, 241, 178, 253, 150, 312, 176, 269, 149, 336, 224, 395, 192, 309, 216, 381, 207, 592, 230, 336, 239, 497, 312, 481, 266, 405, 348, 526, 270, 549, 317, 497, 277, 570, 354, 532, 334

Offset: 1

Justus Springer, Aug 04 2023

nonn

This sequence appears in Proposition 7.1, p. 27 of Haettig, Hafner, Hausen and Springer.

Justus Springer, Table of n, a(n) for n = 1..200
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.
Daniel Hättig, Jürgen Hausen, Justus Springer and Hendrik Süß, Log del Pezzo surfaces with torus action - a searchable database

Cf. A145582, A145581.

cp's OEIS Frontend

A145581 Number of isomorphism classes of toric log del Pezzo surfaces with index L = n.

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