The determinant bundle on the moduli space of stable triples over a curve (Q1857376)

Given a closed Riemann surface \(X\) there is the moduli space of triples \((E_{1},E_{2},\varphi)\), where \(E_{1}\) and \(E_{2}\) are holomorphic vector bundles over \(X\) and \(\varphi:E_{1} \to E_{2}\) is a holomorphic vector bundle homomorphism. The authors construct a holomorphic Hermitian line bundle over such moduli space and compute the curvature of the Chern connection, showing that this is a constant times the natural Kähler form on the moduli space.