Sarti surface

In algebraic geometry, a Sarti surface is a degree-12 nodal surface with 600 nodes, found by Alessandra Sarti in 1999 and published by her in 2001. The maximal possible number of nodes of a degree-12 surface is not known (as of 2015), though Yoichi Miyaoka showed that it is at most 645.

Sarti has also found sextic, octic and dodectic nodal surfaces with high numbers of nodes and high degrees of symmetry.

Sextic with 48 node
Sextic with 48 node
Octic with 72 nodes
Octic with 144 nodes
Dodectic surface with 360 nodes
3D model of Sarti surface

References

Sarti, Alessandra (2001), "Pencils of symmetric surfaces in $\mathbb {P} _{3}$ ", Journal of Algebra, 246 (1): 429–452, arXiv:math/0106080, doi:10.1006/jabr.2001.8953, MR 1872630
Sarti, Alessandra (1 December 2001), "Pencils of Symmetric Surfaces in P3", Journal of Algebra, 246 (1): 429–452, arXiv:math/0106080, doi:10.1006/jabr.2001.8953, ISSN 0021-8693, S2CID 17214934
Sarti, Alessandra (2008), "Symmetrische Flächen mit gewöhnlichen Doppelpunkten", Mathematische Semesterberichte, 55 (1): 1–5, doi:10.1007/s00591-007-0030-2, ISSN 0720-728X, MR 2379658, S2CID 122576773
Miyaoka, Yoichi (1984), "The maximal number of quotient singularities on surfaces with given numerical invariants", Mathematische Annalen, 268 (2): 159–171, doi:10.1007/bf01456083, MR 0744605, S2CID 121817163