Toric and tropical Bertini theorems in positive characteristic

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

Toric and tropical Bertini theorems in positive characteristic

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

School of Mathematics

Research output: Working paper › Preprint

Abstract / Description of output

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.

Original language	English
Publisher	ArXiv
Publication status	Published - 25 Nov 2021

Keywords / Materials (for Non-textual outputs)

math.AG
math.AC
14M25 (Primary), 12J25, 13A35, 14T15 (Secondary)

Access to Document

2111.13214v1Submitted manuscript, 301 KB

https://arxiv.org/abs/2111.13214

Cite this

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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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T1 - Toric and tropical Bertini theorems in positive characteristic

AU - Gandini, Francesca

AU - Hering, Milena

AU - Maclagan, Diane

AU - Mohammadi, Fatemeh

AU - Rajchgot, Jenna

AU - Wheeler, Ashley K.

AU - Yu, Josephine

PY - 2021/11/25

Y1 - 2021/11/25

N2 - 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.

AB - 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.

KW - math.AG

KW - math.AC

KW - 14M25 (Primary), 12J25, 13A35, 14T15 (Secondary)

M3 - Preprint

BT - Toric and tropical Bertini theorems in positive characteristic

PB - ArXiv

ER -

Toric and tropical Bertini theorems in positive characteristic

Abstract / Description of output

Keywords / Materials (for Non-textual outputs)

Access to Document

Fingerprint

Cite this