Nodal complete intersection threefold with defect

Abstract

In this paper we show that a nodal complete intersection threefold $X$ in $\mathbb{P}^{3+c}$ with defect, but without induced defect, has at least $\sum_{i\leq j} (d_i-1)(d_j-1)$ nodes, provided either $c=2$ or $d_c>\sum_{i=1}^{c-1} d_i$ holds.

This is a modified version of the second part of arXiv:1310.0227v1 [math.AG]. The corresponding part has been left out of arXiv:1310.0227 [math.AG]