Title: Anticanonical tropical del Pezzo cubic surfaces contain exactly 27 lines
Speaker: Maria Angelica Cueto (Ohio State University)
Abstract: Since the beginning of tropical geometry, a persistent challenge has been to emulate tropical versions of classical results in algebraic geometry. The well-know statement "any smooth surface of degree three in $P^3$ contains exactly 27 lines'' is known to be false tropically. Work of Vigeland from 2007 provides examples of tropical cubic surfaces with infinitely many lines and gives a classification of tropical lines on general smooth tropical surfaces in $TP^3$. In this talk I will explain how to correct this pathology by viewing the surface as a del Pezzo cubic and considering its embedding in $P^{44}$ via its anticanonical bundle. The combinatorics of the root system of type $E_6$ and a tropical notion of convexity will play a central role in the construction. This is joint work in progress with Anand Deopurkar.
Seminar URL: https://research.math.osu.edu/agseminar/
