The momentum polytope of actions on contact manifolds via toric varieties

TL;DR

This paper explores the convexity of momentum polytopes in contact manifolds, leveraging their isomorphism to specific varieties, and connects contact geometry with toric varieties.

Contribution

It establishes a link between contact manifolds and toric varieties, demonstrating convexity of momentum polytopes via isomorphism results.

Findings

Momentum polytopes of contact manifolds are convex.

Contact varieties are isomorphic to certain algebraic varieties.

The convexity follows from the isomorphism to toric varieties.

Abstract

Due to a previous result which states that contact varieties are isomorphic to certain varieties, the momentum polytopes of contact manifolds are convex.