Quillen determinant line bundle

In mathematics, the Quillen determinant line bundle is a line bundle over the space of Cauchy–Riemann operators of a vector bundle over a Riemann surface, introduced by Quillen (1985). Quillen proved the existence of the Quillen metric on the determinant line bundle, a Hermitian metric defined using the analytic torsion of a family of differential operators.

See also

• Quillen metric

References

• Quillen, Daniel (1985), "Determinants of Cauchy-Riemann operators over a Riemann surface", Functional Analysis and Its Applications, 19, Springer New York: 31–34, doi:10.1007/BF01086022, ISSN 0016-2663, MR 0783704