Toric and tropical Bertini theorems in positive characteristic
Francesca Gandini, Milena Hering, Diane Maclagan, Fatemeh Mohammadi,, Jenna Rajchgot, Ashley K. Wheeler, and Josephine Yu

TL;DR
This paper extends classical Bertini theorems to positive characteristic settings, introducing new algebraic tools and broadening the applicability of tropical geometry results.
Contribution
It generalizes the toric Bertini theorem to positive characteristic and extends the tropical Bertini theorem to all characteristics, removing previous restrictions.
Findings
Generalization of toric Bertini theorem to positive characteristic
Extension of tropical Bertini theorem to arbitrary characteristic
Removal of characteristic dependence in tropical connectivity results
Abstract
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 \kk(t_1,\dots,t_d) of rational functions over an algebraically closed field \kk 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.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsPolynomial and algebraic computation · Algebraic Geometry and Number Theory · Commutative Algebra and Its Applications
