20 citations · 69 across the 18 of their papers we have counts for
21 papers
Maximal singular curves over finite fields from elliptic and hyperelliptic curves
Cesar Hilario, Rodrigo Salomão, Renato Vidal Martins
We construct explicit families of maximal singular curves over finite fields. A maximal singular curve is a curve that attains the Aubry-Perret bound, which is the natural extensio…
Towards Brill--Noether theory for cuspidal curves
Ethan Cotterill, Renato Vidal Martins
Understanding when an abstract complex curve of given genus comes equipped with a map of fixed degree to a projective space of fixed dimension is a foundational question; and Brill…
Certified Severi dimensions for hyperelliptic and supersymmetric cusps
Ethan Cotterill, Vinícius Lima, Renato Vidal Martins +1
In a previous paper, the first three authors formulated a precise conjecture about the dimension of the {\it generalized Severi variety} of degree-…
On Gonality and Canonical Models of Unicuspidal Rational Curves
Naamã Galdino, Renato Vidal Martins, Danielle Nicolau
We study the gonality and canonical model of a rational unicuspidal curve C. We are mainly interested in the case where C is non-Gorenstein. We classify such curves via different n…
Max Noether Theorem for Singular Curves
Edson Martins Gagliardi, Renato Vidal Martins
Max Noether's Theorem asserts that if is the dualizing sheaf of a nonsingular nonhyperelliptic projective curve, then the natural morphisms are…
Severi dimensions for unicuspidal curves
Ethan Cotterill, Vinícius Lara Lima, Renato Vidal Martins
We study parameter spaces of linear series on projective curves in the presence of unibranch singularities, i.e. {\it cusps}; and to do so, we stratify cusps according to value sem…