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arXiv · 2111.13214

Toric and tropical Bertini theorems in positive characteristic

Francesca Gandini·Milena Hering·Diane Maclagan·Fatemeh Mohammadi·Jenna Rajchgot·Ashley K. Wheeler·Josephine Yu
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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.

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Francesca Gandini, Milena Hering, Diane Maclagan, Fatemeh Mohammadi, Jenna Rajchgot, Ashley K. Wheeler, Josephine Yu. 2021-11-25. Toric and tropical Bertini theorems in positive characteristic. https://arxiv.org/abs/2111.13214

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