Random Toric Surfaces and a Threshold for Smoothness

TL;DR

This paper introduces a probabilistic model for toric surfaces inspired by random graphs and investigates the threshold at which these surfaces transition from singular to smooth.

Contribution

It proposes a novel random model for toric surfaces and analyzes the critical threshold for smoothness within this framework.

Findings

Identifies a specific threshold probability for smoothness

Demonstrates phase transition behavior in surface properties

Provides probabilistic estimates for smoothness occurrence

Abstract

We present a notion of a random toric surface modeled on a notion of a random graph. We then study some threshold phenomena related to the smoothness of the resulting surfaces.