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.
![](http://up.wiki.x.io/wikipedia/commons/thumb/d/d5/Sarti_surface.png/240px-Sarti_surface.png)
Sarti has also found sextic, octic and dodectic nodal surfaces with high numbers of nodes and high degrees of symmetry.
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Sextic with 48 node
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Sextic with 48 node
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Octic with 72 nodes
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Octic with 144 nodes
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Dodectic surface with 360 nodes
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3D model of Sarti surface
See also
editReferences
edit- Sarti, Alessandra (2001), "Pencils of symmetric surfaces in ", 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