English

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}
}