Quotients of smooth projective toric varieties by $\mu_p$ in positive characteristics $p$

TL;DR

This paper proves that when smooth projective toric varieties are quotiented by the group scheme μ_p in positive characteristic p, the resulting varieties remain toric, preserving their combinatorial structure.

Contribution

It establishes that quotients of smooth projective toric varieties by μ_p in positive characteristic are themselves toric varieties, a result not previously confirmed.

Findings

Quotients by μ_p are toric varieties.

Preservation of toric structure under group quotient.

Applicable in positive characteristic algebraic geometry.

Abstract

In this paper we show that quotients of smooth projective toric varieties by $\mu_p$ in positive characteristics $p$ are toric varieties.