Terracini loci of curves

Abstract

AbstractWe study subsets S of curves X whose double structure does not impose independent conditions to a linear series L, but there are divisors $$D\in |L|$$ D ∈ | L | singular at all points of S. These subsets form the Terracini loci of X. We investigate Terracini loci, with a special look towards their non-emptiness, mainly in the case of canonical curves, and in the case of space curves.