Youngook Choi

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math.AG2026

Universal extension spaces and modular maps: unveiling irreducible components of Brill-Noether loci of stable bundles on a general $I^½$ -gonal curve

Youngook Choi, Flamino Flamini, Seonja Kim

We investigate the Brill-Noether theory of rank-two, degree- $d$ stable vector bundles of speciality $3$ on a general $I^½$ -gonal curve of genus $g$ , $3 \leq Î½< \lfloor \frac{g+3}{2…

math.AG2026

Complete classification of irreducible components of the Brill-Noether locus of rank- $2$ vector bundles of degree $d$ and speciality $2$ on a general $I^½$ -gonal curve

Youngook Choi, Flaminio Flamini, Seonja Kim

This paper replaces the previous longer version and focuses on the specialty $2$ case. More precisely, in this paper we address the Brill-Noether theory for rank-two, degree $d$ st…

math.AG2026

Decomposition of the Tschirnhausen module for coverings on decomposable $P^{1}$ -bundles

Youngook Choi, Hristo Iliev, Seonja Kim

In this note, we show that for a smooth algebraic variety $Y$ and a smooth $m$ -section $X$ of the $P^{1}$ -bundle \[ f : \mathbb{P}(\mathcal{O}_Y \oplus \mathcal{O}_Y(E)) \lo…

math.AG2025

On the Tschirnhausen module of coverings of curves on decomposable ruled surfaces and applications

Youngook Choi, Hristo Iliev, Seonja Kim

We show that for two classes of $m$ -secant curves $X \subset S$ , with $m \geq 2$ , where $f : S = P (O_{Y} \oplus O_{Y} (E)) \to Y$ and $E$ is a non-special…

math.AG2024

Components of the Hilbert Scheme of smooth projective curves using ruled surfaces II: existence of non-reduced components

Youngook Choi, Hristo Iliev, Seonja Kim

For $I^^{3} \geq 7$ and $g \geq 6 I^^{3} + 5$ , we construct a family $F^{'}$ of curves lying on cones in $P^{g - 3 I^^{3} + 1}$ over smooth non-degenerate curves of genus $I^^{3}$ …

Universal extension spaces and modular maps: unveiling irreducible components of Brill-Noether loci of stable bundles on a general I^½-gonal curve

Complete classification of irreducible components of the Brill-Noether locus of rank-2 vector bundles of degree d and speciality 2 on a general I^½-gonal curve

Decomposition of the Tschirnhausen module for coverings on decomposable P1-bundles

On the Tschirnhausen module of coverings of curves on decomposable ruled surfaces and applications

Components of the Hilbert Scheme of smooth projective curves using ruled surfaces II: existence of non-reduced components

Universal extension spaces and modular maps: unveiling irreducible components of Brill-Noether loci of stable bundles on a general $I^½$ -gonal curve

Complete classification of irreducible components of the Brill-Noether locus of rank- $2$ vector bundles of degree $d$ and speciality $2$ on a general $I^½$ -gonal curve

Decomposition of the Tschirnhausen module for coverings on decomposable $P^{1}$ -bundles