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
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  Octic with 72 nodes
• 
  Octic with 144 nodes
• 
  Dodectic surface with 360 nodes
• 
  3D model of Sarti surface

See also

• Nodal 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

External links

• Sarti surfaces
• Weisstein, Eric W., "Sarti Dodecic", MathWorld