Quillen, Daniel Determinants of Cauchy-Riemann operators on a Riemann surface. (English. Russian original) Zbl 0603.32016 Funct. Anal. Appl. 19, 31-34 (1985); translation from Funkts. Anal. Prilozh. 19, No. 1, 37-41 (1985). The author considers on a smooth vector bundle over a compact Riemann surface the space of \(\overline{\partial}\) operators (corresponding to the possible complex structures) and constructs on this space a determinant by using the concepts of a determinant line bundle and the determinant of an elliptic operator. Cited in 13 ReviewsCited in 198 Documents MSC: 32F99 Geometric convexity in several complex variables 58J99 Partial differential equations on manifolds; differential operators 30F10 Compact Riemann surfaces and uniformization Keywords:determinants of Cauchy-Riemann operators; determinant line bundle; determinant of an elliptic operator PDFBibTeX XMLCite \textit{D. Quillen}, Funct. Anal. Appl. 19, 31--34 (1985; Zbl 0603.32016); translation from Funkts. Anal. Prilozh. 19, No. 1, 37--41 (1985) Full Text: DOI References: [1] D. Ray and I. Singer, ”Analytic torsion,” Ann. Math.,98, No. 1, 154-177 (1973). · Zbl 0267.32014 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.