Ashley K. Wheeler, Georgia Tech
Authors: Francesca Gandini, Milena Hering, Diane Maclagn, Fatemeh Mohammadi, Jenna Rajchgot, Ashley K. Wheeler, Josephine Yu
2022 AWM Research Symposium
Homological and Combinatorial Aspects of Commutative Algebra

We generalize the toric Bertini theorem of Fuchs, Mantova, and Zannier to positive characteristic. A key part of the proof is a new algebraically closed field containing the field $k(t_1,\dots,t_d)$ of rational functions over an algebraically closed field $k$ of prime characteristic. As a corollary, we extend the tropical Bertini theorem of Maclagan and Yu to arbitrary characteristic, which removes the characteristic dependence from the $d$-connectivity result for tropical varieties from that paper.

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