A Taste of Extremal Combinatorics in AG

Algebra Seminar
Tuesday, December 7, 2021 - 10:00am for 1 hour (actually 50 minutes)
Skiles 006
Robert Walker – University of Wisconsin, Madison – robmarsw785@gmail.com
Ashley K. Wheeler

In this talk, we survey known results and open problems tied to the dual graph of a projective algebraic F-scheme over a field F, a construction that apparently Janos Kollar is familiar with. In particular one can use this construction to answer the following question: if you consider the 27 lines on a cubic surface in P^3, how many lines meet a given line? The dual graph can answer this and more questions in enumerative geometry and intersection theory easily, based on work of Benedetti -- Varbaro and others.