Stable vector bundles on the families of curves

TL;DR

This paper introduces a novel approach to proving the Chen-Donaldson-Sun theorem, focusing on stable vector bundles over families of curves, with implications for special metrics and moduli space cycles.

Contribution

It presents a new method for establishing the Chen-Donaldson-Sun theorem and explores the construction of special metrics on stable bundles over surface families.

Findings

Demonstrates the new approach with examples

Establishes a connection between special metrics and moduli space cycles

Provides insights into stable vector bundles on surface families

Abstract

We offer a new approach to proving the Chen-Donaldson-Sun theorem which we demonstrate with a series of examples. We discuss the existence of a construction of a special metric on stable vector bundles over the surfaces formed by a families of curves and its relation to the one-dimensional cycles in the moduli space of stable bundles on curves.