Cech cover of the complement of the discriminant variety. Part II: Deformations of Gaussskizze
Abstract
The configuration space of $n$ marked points on the complex plane is considered. We investigate a decomposition of this space by socalled Gaussskizze i.e. a class of graphs being forests, introduced by Gauss. It is proved that this decomposition is a semialgebraic topological stratification. It also forms a cell decomposition of the configuration space of $n$ marked points. Moreover, we prove that classical tools from deformation theory, ruled by a MaurerCartan equation, can be used only locally for Gaussskizze. We prove that the deformation of the Gaussskizze is governed by a HamiltonJacobi differential equation. This gives developments concerning Saito's Frobenius manifold. Finally, a Gaussskizze operad is introduced. It is an enriched FultonMacPherson operad, topologically equivalent to the little 2disc operad.
 Publication:

arXiv eprints
 Pub Date:
 July 2020
 arXiv:
 arXiv:2007.01604
 Bibcode:
 2020arXiv200701604C
 Keywords:

 Mathematics  Algebraic Geometry;
 Mathematics  Algebraic Topology