# Sarti surface

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{{Short description|Algebraic surface of degree 12}}
right|240px

In [algebraic geometry](/source/algebraic_geometry), a '''Sarti surface''' is a degree-12 [nodal surface](/source/nodal_surface) with 600 nodes, found by [Alessandra Sarti](/source/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](/source/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.

<gallery>
File:Sarti sextic 48 A.png|Sextic with 48 node
File:Sarti sextic 48 (Stabchen).png|Sextic with 48 node
File:Sarti's Octic with 72.png|Octic with 72 nodes
File:Sarti's octic with 144 nodes.png|Octic with 144 nodes
File:Sarti dodectic 360.png|Dodectic surface with 360 nodes
File:3D model of Sarti surface.stl|3D model of Sarti surface
</gallery>

==See also==
*[Nodal surface](/source/Nodal_surface)

==References==
*{{citation
 | last = Sarti | first = Alessandra | author-link = Alessandra Sarti
 | arxiv = math/0106080
 | doi = 10.1006/jabr.2001.8953
 | issue = 1
 | journal = Journal of Algebra
 | mr = 1872630
 | pages = 429–452
 | title = Pencils of symmetric surfaces in <math>\mathbb{P}_3</math>
 | volume = 246
 | year = 2001}}
*{{citation|  last1=Sarti | first1=Alessandra | author-link = Alessandra Sarti | title=Pencils of Symmetric Surfaces in P3|url=https://www.sciencedirect.com/science/article/pii/S0021869301989537|journal=Journal of Algebra|date=1 December 2001|issn=0021-8693|pages=429–452|volume=246|issue=1|doi=10.1006/jabr.2001.8953|arxiv=math/0106080| s2cid=17214934 }}
*{{Citation | last1=Sarti | first1=Alessandra | title=Symmetrische Flächen mit gewöhnlichen Doppelpunkten |mr=2379658 | year=2008 | journal=Mathematische Semesterberichte | issn=0720-728X | volume=55 | issue=1 | pages=1–5|
doi=10.1007/s00591-007-0030-2| s2cid=122576773 }}
*{{Citation | last=Miyaoka | first=Yoichi |authorlink =Yoichi Miyaoka |  title=The maximal number of quotient singularities on surfaces with given numerical invariants | year=1984 | journal=[Mathematische Annalen](/source/Mathematische_Annalen) | volume=268 | issue=2 | pages=159–171 | doi=10.1007/bf01456083|mr=0744605 | s2cid=121817163 }}

==External links==
*{{citation|url=http://enriques.mathematik.uni-mainz.de/docs/Esarti.shtml |title=Sarti surfaces}}
*{{mathworld|id=SartiDodecic|title=Sarti Dodecic|mode=cs2}}

Category:Algebraic surfaces
Category:Complex surfaces

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Adapted from the Wikipedia article [Sarti surface](https://en.wikipedia.org/wiki/Sarti_surface) by Wikipedia contributors ([contributor history](https://en.wikipedia.org/wiki/Sarti_surface?action=history)). Available under [Creative Commons Attribution-ShareAlike 4.0 International](https://creativecommons.org/licenses/by-sa/4.0/). Changes may have been made.