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Algebraic Geometry Seminar - Angelica Cueto

Pilar
October 9, 2018
3:00PM - 4:00PM
Math Tower 154

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Add to Calendar 2018-10-09 15:00:00 2018-10-09 16:00:00 Algebraic Geometry Seminar - Angelica Cueto 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/ Math Tower 154 Department of Mathematics math@osu.edu America/New_York public

Title: Anticanonical tropical del Pezzo cubic surfaces contain exactly 27 lines

SpeakerMaria 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 URLhttps://research.math.osu.edu/agseminar/

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