## View abstract

### Session S31 - Mathematical-Physical Aspects of Toric and Tropical Geometry

Tuesday, July 13, 11:00 ~ 12:00 UTC-3

## The spine of the $T$-graph of the Hilbert scheme of points

### Diane Maclagan

The torus $T$ of projective space also acts on the Hilbert scheme of subschemes of projective space, and the $T$-graph of the Hilbert scheme has vertices the fixed points of this action, and edges the closures of one-dimensional orbits. In general this graph depends on the underlying field. I will discuss joint work with Rob Silversmith, in which we construct of a subgraph, which we call the spine, of the $T$-graph of $\mathrm{Hilb}^N(\mathbb A^2)$ that is independent of the choice of infinite field. A key technique is an understanding of the tropical ideal, in the sense of tropical scheme theory, of the ideal of the universal family of an edge in the spine.