arXiv subjects

Frederico Sercio

Publications and source records attributed to Frederico Sercio.

3 recordsLinked to original sources

arXiv2020

Characterizing gonality for two-component stable curves

It is a well-known result that a stable curve of compact type over $\mathbb{C}$ having two components is hyperelliptic if and only if both components are hyperelliptic and the point of intersection is a Weierstrass point for each of them. With the use of admissible covers, we generalize this characterization in two ways: for stable curves of higher gonality having two smooth components and one node; and for hyperelliptic and trigonal stable curves having two smooth non rational components and any number of nodes.

math.AG↗

arXiv2019

On the gonality of stable curves

In this paper we use admissible covers to investigate the gonality of a stable curve $C$ over $\mathbb{C}$. If $C$ is irreducible, we compare its gonality to that of its normalization. If $C$ is reducible, we compare its gonality to that of its irreducible components. In both cases we obtain lower and upper bounds. Furthermore, we show that four admissible covers constructed give rise to generically injective maps between Hurwitz schemes. We show that the closures of the images of three of these maps are components of the boundary of the target Hurwitz schemes, and the closure of the image of the remaining map is a component of a certain codimension-1 subscheme of the boundary of the target Hurwitz scheme.

math.AG↗

arXiv2018

On the degree-1 Abel map for nodal curves

Let $C$ be a nodal curve and $L$ be an invertible sheaf on $C$. Let $α_{L}:C\dashrightarrow J_{C}$ be the degree-$1$ rational Abel map, which takes a smooth point $Q\in C$ to $\left[ m_{Q}\otimes L\right] $ in the Jacobian of $C$. In this work we extend $α_{L}$ to a morphism $\overlineα_{L}:C\rightarrow\overline{J}_{E}^{P}$ taking values on Esteves' compactified Jacobian for any given polarization $E$. The maps $\overlineα_{L}$ are limits of Abel maps of smooth curves of the type $α_{L}$.

math.AG↗