In
algebraic geometry, a Sarti surface is a degree-12
nodal surface
In algebraic geometry, a nodal surface is a surface in (usually complex) projective space whose only singularities are nodes. A major problem about them is to find the maximum number of nodes of a nodal surface of given degree.
The following t ...
with 600 nodes, found by . The maximal possible number of nodes of a degree-12 surface is not known (as of 2015), though
Yoichi Miyaoka
is a mathematician who works in algebraic geometry and who proved (independently of Shing-Tung Yau's work) the Bogomolov–Miyaoka–Yau inequality in an Inventiones Mathematicae paper.
In 1984, Miyaoka extended the Bogomolov–Miya ...
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.
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
See also
*
Nodal surface
In algebraic geometry, a nodal surface is a surface in (usually complex) projective space whose only singularities are nodes. A major problem about them is to find the maximum number of nodes of a nodal surface of given degree.
The following t ...
References
*
*
*
External links
*
*{{mathworld, id=SartiDodecic, title=Sarti Dodecic
Algebraic surfaces
Complex surfaces