arXiv subjects
Publications and source records attributed to Lia Feital.
We propose a version of the Enriques-Babagge Theorem for a singular curve $C$, involving its canonical model $C'$. We provide a partial proof for an arbitrary curve $C$ and complete the proof for unicuspidal monomial curves by describing the generators of the ideal of $C'\subset\mathbb{P}^{g-1}$.
We study the Clifford dimension of an integral curve. To do so, we extend the notion of Clifford index, allowing torsion-free sheaves on its computation. We derive results for arbitrary curves, and then focus on the monomial case. In this context, we obtain combinatorial formulae for the Clifford index and apply them to the case of Clifford dimension $2$.
We study singular rational curves in projective space, deducing conditions on their parametrizations from the value semigroups $\sss$ of their singularities. In particular, we prove that a natural heuristic for the codimension of the space of nondegenerate rational curves of arithmetic genus $g>0$ and degree $d$ in $\mb{P}^n$, viewed as a subspace of all degree-$d$ rational curves in $\mb{P}^n$, holds whenever $g$ is small. On the other hand, we show that this heuristic fails in general, by exhibiting an infinite family of examples of Severi-type varieties of rational curves containing "excess" components of dimension strictly larger than the space of $g$-nodal rational curves.
In this article we study rational curves with a unique unibranch genus-$g$ singularity, which is of {\it $\ka$-hyperelliptic} type in the sense of \cite{To}; we focus on the cases $\ka=0$ and $\ka=1$, in which the semigroup associated to the singularity is of (sub)maximal weight. We obtain a partial classification of these curves according to the linear series they support, the scrolls on which they lie, and their gonality.