# Holomorphic aspects of moduli of representations of quivers

Research paper by Pradeep Das, S. Manikandan, N. Raghavendra

Indexed on: 11 Nov '17Published on: 11 Nov '17Published in: arXiv - Mathematics - Algebraic Geometry

#### Abstract

This article describes some complex-analytic aspects of the moduli space of the finite-dimensional complex representations of a finite quiver, which are stable with respect to a fixed rational weight. We construct a natural structure of a complex manifold on this moduli space, and a K\"ahler metric on the complex manifold. We then define a Hermitian holomorphic line bundle on the moduli space, and show that its curvature is a rational multiple of the K\"ahler form.