arXiv subjects
Publications and source records attributed to İrfan Kadıköylü.
We study the variety of rank $\leq k$ quadrics containing a general projective curve and show that it has the expected dimension in the range $g-d+r\leq 1$. By considering the loci where this expectation is not true, we construct new divisor classes in $\overline{\mathcal{M}}_{g,n}$. We use one of these classes to show that $\overline{\mathcal{M}}_{15,9}$ is of general type.
We compute the class of the effective divisors on $\overline{\mathcal{M}}_{g,n}$, which are set theoretically equal to the locus of moduli points $[C,p_1,\dots ,p_n]$ where $C$ lies on a quadric under the map given by the linear series $|K_C-p_1-\dots -p_n|$. Using this divisor class we show that the moduli spaces $\overline{\mathcal{M}}_{16,8}$ and $\overline{\mathcal{M}}_{17,8}$ are of general type. We also note that the divisor classes computed in the papers \cite{FV1} and \cite{FV2} can be used to show that $\overline{\mathcal{M}}_{12,10}$ is of general type as well.