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Tropical Algebraic Geometry - A tropical count of binodal cubic surfaces

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Tropical Algebraic Geometry - A tropical count of binodal cubic surfaces
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In this talk I will give a short introduction to tropical algebraic geometry based on a tropical count of binodal cubic surfaces (joint work with Madeline Brandt). There are 280 binodal cubic surfaces through 17 points in general position. They can be counted using tropical geometry. After a brief introduction into tropical geometry we see how the dual subdivision of the Newton polytope allows us to count surfaces through points in Mikhalkin position via floor plans. We will see that we can recover 214 binodal surfaces with separated nodes in their tropicalizations and we will also have a short look at the complexes hiding the remaining 66 surfaces.
Keywords Tropical Geometry Enumerative Geometry binodal cubic surfaces
Surface Geometry Algebraic number Mathematical optimization
Surface Rational number Conic section Number theory Weight Mathematical singularity Maxima and minima Curve Dreiecksnetz Geometry Duality (mathematics) Polytop Object (grammar) Cubic graph Glattheit <Mathematik> Vertex (graph theory) Configuration space Binodal Linear map Unimodulare Matrix Polynomial Geometry Tropische Geometrie Correspondence (mathematics) Valuation (algebra) Algebraic number Point (geometry) Complex (psychology) Enumerated type Plane (geometry) Theorem Acoustic shadow Condition number Block (periodic table) Combinatorics
Surface Duality (mathematics) Polytop Weight Point (geometry) Complex (psychology) Cubic graph Vertex (graph theory) Configuration space Enumerated type Dreiecksnetz Binodal
Surface Cubic graph Enumerated type Binodal
Surface Coefficient Kettenkomplex Mathematical singularity Point (geometry) Cubic graph Hausdorff dimension Theorem Enumerated type Binodal
Surface Kettenkomplex Cubic graph Vertex (graph theory) Enumerated type Binodal
Surface Geometry Linear algebra Tropische Geometrie Kettenkomplex Algebraic number Point (geometry) Theory Curve Enumerated type Flächensingularität Planar graph Geometry Hausdorff space Canadian Mathematical Society Cubic graph Partial derivative Vertex (graph theory) Multiplication Binodal Hyperplane