Oliveira, Gilvan; Viana, Paulo Theta characteristics in trigonal curves. (English) Zbl 1096.14023 Commun. Algebra 33, No. 11, 3939-3948 (2005). Let \(C\) be a trigonal curve of genus \(g\geq 5\). Let \(m\) and \(n\) be the invariants of \(C\). The authors show: (1) If \(m<2r\leq n\), then \(C\) has a theta characteristic of type \(g^{r}_{g-1}\) if and only if the exceptional divisor can be written as \(E=2F+\sum Q\), where the last summation has \(n-2r\) distinct points \(Q\not\in \text{ supp}(F)\) such that the trigonal divisor over \(Q\) is ramified;(2) If \(n-m-1>r\), then \(C\) does not admit a theta characteristic of dimension \(r\); (3) If \(n-m-1\leq r\), then the dimension of the moduli space of trigonal curves of genus \(g\) (with invariants \(m\) and \(n\)) and having a theta characteristic of dimension \(r\) is \(g+m+r+3\). Reviewer: Fernando Torres (Campinas) MSC: 14H45 Special algebraic curves and curves of low genus 14H05 Algebraic functions and function fields in algebraic geometry 14H51 Special divisors on curves (gonality, Brill-Noether theory) 14C20 Divisors, linear systems, invertible sheaves Keywords:special divisors; theta characteristics; trigonal curves PDFBibTeX XMLCite \textit{G. Oliveira} and \textit{P. Viana}, Commun. Algebra 33, No. 11, 3939--3948 (2005; Zbl 1096.14023) Full Text: DOI References: [1] Andreotti A., Ann. Scuola Norm. Sup. Pisa 21 pp 189– (1967) [2] Arbarello A., Geometry of Algebraic Curves (1985) · Zbl 0559.14017 · doi:10.1007/978-1-4757-5323-3 [3] Coppens M., Indag. Math. 47 pp 245– (1985) [4] Hartshorne R., Algebraic Geometry (1977) [5] Hensel K., Theory der algebraischen Funktionen einer Variablen (1902) [6] DOI: 10.1007/BF02418090 · Zbl 0061.35407 · doi:10.1007/BF02418090 [7] DOI: 10.1007/BF02941515 · Zbl 0628.14029 · doi:10.1007/BF02941515 [8] Mumford D., Ann. Scient. Éc. Norm. Sup. 4 série 4 pp 181– (1971) [9] DOI: 10.1016/0022-4049(92)90135-3 · Zbl 0768.14016 · doi:10.1016/0022-4049(92)90135-3 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.