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Montserrat Vite

Publications and source records attributed to Montserrat Vite.

6 recordsLinked to original sources
arXiv2026

Curves contained in a quartic determinantal surface containing a line

Let $X\subseteq \mathbb{P}^{3}$ be a very general element of the Noether-Lefschetz divisor that parametrizing smooth quartic surfaces containing a line. Let $L\subseteq X$ denote the corresponding line. We study the curves contained in $X$ and analyze their behavior in the Hilbert scheme. We first determine which linear systems contain smooth irreducible curves. For most classes, we verify that the general member is a smooth point of the expected Hilbert scheme. Finally we compute the Rao function of any curve on $X$.

math.AG↗
arXiv2026

The classification of ACM curves on a surface in $\mathbb{P}^{3}$

We classify ACM curves contained in a surface of degree d in $\mathbb{P}^{3}$ in terms of weak admissible pairs. In the case of a very general smooth determinantal quartic surface, we provide a geometric description of these curves and compute their Picard classes on the surface. Finally, we present a generalization to ACM closed subvarieties of codimension $1$ on a hypersurface in $\mathbb{P}^{n}$.

math.AG↗
arXiv2025

Explicit birational geometry of determinantal quartic 3-folds

A general linear determinantal quartic in $\mathbb{P}^4$ is nodal, non-$\mathbb{Q}$-factorial and rational. We show that the family $\mathcal{F}$ of such quartics also contains rational $\mathbb{Q}$-factorial quartics, and that a generic member of $\mathcal{F}$ can specialize to a rational non-$\mathbb{Q}$-factorial double quadric. We prove that the birational geometry of these three types of 3-folds is governed by the extrinsic geometry of a curve $C\subset \mathbb{P}^3$ of degree 10 and genus 11.

math.AG↗
arXiv2023

The Noether-Lefschetz locus of surfaces in $\mathbb{P}^3$ formed by determinantal surfaces

We compute the dimension of certain components of the family of smooth determinantal degree $d$ surfaces in $\mathbb{P}^3$, and show that each of them is the closure of a component of the Noether-Lefschetz locus $NL(d)$. Our computations exhibit that smooth determinantal surfaces in $\mathbb{P}^3$ of degree 4 form a divisor in $|\mathcal{O}_{\mathbb{P}^3}(4)|$ with 5 irreducible components. We will compute the degrees of each of these components: $320,2508,136512,38475$ and $320112$.

math.AG↗
arXiv2023

Liaison theory and the birational geometry of the Hilbert scheme of curves in $\mathbb{P}^{3}$

In the Hilbert scheme of curves of degree $d_{r}=\frac{r(r+1)}{2}$ and arithmetic genus $g_{r}=\frac{r(r+1)(2r-5)}{6}+1$ in $\mathbb{P}^{3}$ we prove that there exists a unique component of arithmetically Cohen-Macaulay curves denoted by $\overline{\mathscr{C}_{r}}$. For $r\geq 3$, we verify that the subvariety of curves in $\overline{\mathscr{C}_{r}}$ with Rao module of rank one always contains a reducible divisor. In particular, in the case of curves of degree $6$ and genus $3$ we prove that this subvariety is a reducible divisor. Furthermore, the components of such divisor are linearly independent and each component generates an extremal ray of the effective cone $\overline{\text{Eff}(\mathscr{C}_{3})}$.

math.AG↗