The solvable monodromy extension property and varieties of log general type

TL;DR

This paper explores the connection between the solvable monodromy extension property and log canonical models, using the moduli space of smooth curves as a key example to illustrate the relationship.

Contribution

It proposes a speculative link between SME property and log canonical models, supported by the example of moduli spaces of curves and their compactifications.

Findings

Moduli space of smooth curves has SME property.

Maximal SME compactification matches the log canonical model.

Illustrates the relationship between monodromy and log geometry.

Abstract

We speculate on the relationship between the solvable monodromy extension (SME) property and log canonical models. A motivating example is the moduli space of smooth curves which, by earlier work, is known to have this SME property. In this case the maximal SME compactification is the moduli space of stable nodal curves which coincides with its log canonical model.