Toric and tropical Bertini theorems in positive characteristic
Algebraic Geometry
2021-11-29 v1 Commutative Algebra
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.
Keywords
Cite
@article{arxiv.2111.13214,
title = {Toric and tropical Bertini theorems in positive characteristic},
author = {Francesca Gandini and Milena Hering and Diane Maclagan and Fatemeh Mohammadi and Jenna Rajchgot and Ashley K. Wheeler and Josephine Yu},
journal= {arXiv preprint arXiv:2111.13214},
year = {2021}
}