Farkas, H. M. Remarks on Clifford indices. (English) Zbl 0651.14018 J. Reine Angew. Math. 391, 213-220 (1988). Let S be a compact Riemann surface of genus \(g\geq 2\). Let r and s be integers with \(0<r\leq s\leq g-1\). The Clifford index of a special divisor on S of (projective) dimension r and degree \(r+s\), is defined as the integer \(s-r\). By the Clifford index of S we mean the smallest of the Clifford indices of special divisors on S. Clifford’s theorem assserts that a surface of Clifford index zero is hyperelliptic, i.e. if there is a special divisor of Clifford index zero then there is a divisor of Clifford index zero and \(r=1.\) One may ask if a similar result holds for higher values of the Clifford index. In the paper under review it is shown that if the Clifford index t is realized with a divisor of degree d satisfying \(3t+2\leq d\leq g-1\), and if \(g>3(t+1)\), then S carries a meromorphic function of order \(t+2.\) Counterexamples to an unrestricted generalisation are discussed, and a proof of Clifford’s theorem is obtained. Reviewer: H.Martens Cited in 2 ReviewsCited in 1 Document MSC: 14H45 Special algebraic curves and curves of low genus 30F10 Compact Riemann surfaces and uniformization Keywords:Clifford index of a special divisor PDFBibTeX XMLCite \textit{H. M. Farkas}, J. Reine Angew. Math. 391, 213--220 (1988; Zbl 0651.14018) Full Text: DOI Crelle EuDML