## 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

#### University of Warwick, United Kingdom   -   This email address is being protected from spambots. You need JavaScript enabled to view it. document.getElementById('cloakd8e548f7a22f58e6dbd280ccab8f3268').innerHTML = ''; var prefix = '&#109;a' + 'i&#108;' + '&#116;o'; var path = 'hr' + 'ef' + '='; var addyd8e548f7a22f58e6dbd280ccab8f3268 = 'd.m&#97;cl&#97;g&#97;n' + '&#64;'; addyd8e548f7a22f58e6dbd280ccab8f3268 = addyd8e548f7a22f58e6dbd280ccab8f3268 + 'w&#97;rw&#105;ck' + '&#46;' + '&#97;c' + '&#46;' + '&#117;k'; var addy_textd8e548f7a22f58e6dbd280ccab8f3268 = 'd.m&#97;cl&#97;g&#97;n' + '&#64;' + 'w&#97;rw&#105;ck' + '&#46;' + '&#97;c' + '&#46;' + '&#117;k';document.getElementById('cloakd8e548f7a22f58e6dbd280ccab8f3268').innerHTML += '<a ' + path + '\'' + prefix + ':' + addyd8e548f7a22f58e6dbd280ccab8f3268 + '\'>'+addy_textd8e548f7a22f58e6dbd280ccab8f3268+'<\/a>';

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.

Joint work with Rob Silversmith (Northeastern, USA).