# Toric Vector Bundles: GAGA and Hodge Theory

## TL;DR

This paper establishes a GAGA correspondence for toric vector bundles on smooth bases and constructs a related Frölicher approximating vector bundle algebraically, bridging complex analytic and algebraic perspectives.

## Contribution

It provides a GAGA-style theorem for toric vector bundles and offers an algebraic construction of the Frölicher approximating bundle, connecting analytic and algebraic methods.

## Key findings

- Proves a GAGA equivalence for toric vector bundles.
- Constructs the Frölicher approximating bundle algebraically.
- Bridges complex analytic and algebraic approaches in toric geometry.

## Abstract

We prove a GAGA-style result for toric vector bundles with smooth base and give an algebraic construction of the Fr\"olicher approximating vector bundle that has recently been introduced by Dan Popovici using analytic techniques.