Nodal complete intersection threefold with defect

TL;DR

This paper establishes a lower bound on the number of nodes in certain nodal complete intersection threefolds with defect, under specific conditions on the codimension and degrees.

Contribution

It provides a new lower bound on the number of nodes for nodal complete intersection threefolds with defect, assuming no induced defect and specific degree conditions.

Findings

Lower bound of nodes given by sum over degrees for certain threefolds

Conditions on codimension and degrees ensure the bound applies

Advances understanding of the singularity structure in algebraic geometry

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.