An invitation to toric degenerations

By Mark Gross, Bernd S Siebert. 2008

60 citations recorded by the source corpus.

This is an expository paper which explores the ideas of the authors' paper "From Affine Geometry to Complex Geometry", arXiv:0709.2290. We explain the basic ideas of the latter paper by going through a large number of concrete, increasingly complicated examples.

Subfields: Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/949a749ff71988ae84028f9ed3cf8313b7c59a4d

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Geometry and Topology

1. Dhruv Ranganathan
2. Mark Gross
3. P. Hacking
4. Bernd S Siebert
5. Renzo Cavalieri
6. Hannah Markwig
7. Martin Ulirsch
8. S. Keel

In Mathematical Physics

1. Mark Gross
2. Bernd S Siebert
3. P. Hacking
4. Hannah Markwig
5. Renzo Cavalieri
6. Dhruv Ranganathan
7. M. Abouzaid
8. L. Katzarkov

Citations in the corpus

• Tropicalizing the space of admissible covers (2014, background): “The connections between tropical geometry and log geometry are being explored by Gross and Siebert, and Ulirsch, see [21, 36].”
• Theta functions on varieties with effective anti-canonical class (2016, background): “κρ(ϕ) ∈Qgp. Example 1.7. To illustrate how the kink can depend on the choice of ρ⊂ρ let us look at the simplest example of an affine manifold with singularities, see Example 1.16 in [GrSi2], or §3.2 in [GrSi5]. There are only two maximal cells, the 2-simplices σ1 := conv{(−1,0),(0,0),(0,1)}, σ2 := con”