H. Iliev

activity

20242026

collaborators

4 papers

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 $I^^{3}$ …

math.AG2024

Non-reduced components of the Hilbert scheme of curves using triple covers

Youngook Choi, Hristo Iliev, Seonja Kim

In this paper we consider curves on a cone that pass through the vertex and are also triple covers of the base of the cone, which is a general smooth curve of genus $I^^{3}$ and degree…

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

Non-reduced components of the Hilbert scheme of curves using triple covers

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