Weierstrass gap sequences and moduli varieties of trigonal curves (Q1194300)

The Weierstrass gap sequence at an unramified point of a trigonal curve is composed by 2 sequences of consecutive integers; such a result was established by \textit{S. J. Kim} [J. Pure Appl. Algebra 63, No. 2, 171-180 (1990; Zbl 0712.14019)]. With this in mind, the authors obtain the following main result: Theorem: Let \(g\), \(\sigma\) and \(\rho\) be integers with \(g\geq 5\) and \(\sigma<g<\rho<2\sigma+2\). Then the moduli space of pointed trigonal curves of genus \(g\) and Weierstrass gap sequence \(1,\dots,\sigma\), \(\sigma+\rho-g+1,\dots,\rho\) has dimension \(2g+3- \rho+\sigma\) provided \(\rho<3\left[{g+1\over 2}\right]+4-\sigma\). In the course of the proof of this result, the authors provide another proof of Kim's result mentioned above.