Jinhyung Park

activity

20232026

collaborators

9 papers

math.AG2026

Graded Betti numbers of general curves of large degree

JeongDon Lee, Li Li, Jinhyung Park

Let $C$ be a smooth projective complex curve of genus $g$ and gonality $k$ , and $L$ be a very ample line bundle on $C$ . When $L$ has sufficiently large degree, the vanishing and no…

math.AG2026

Ulrich sheaves and determinantal representations for higher secant varieties of curves

Daniele Agostini, Mario Kummer, Jinhyung Park

We show that higher secant varieties of smooth projective curves have symmetric admissible determinantal representations with symmetric Ulrich sheaves of rank one if the embedding…

math.AG2026

Effective results on projective normality of the first and second secant varieties

Doyoung Choi, Jinhyung Park

In joint work with Lacini and Sheridan, we proved that the first and second secant varieties of a smooth projective complex variety embedded by the complete linear system of a suff…

math.AG2026

Hilbert polynomials of the first and second secant varieties

Doyoung Choi, Jinhyung Park

In this paper, we give a description of the cohomology groups of the symmetric powers of the tautological bundle associated with a sufficiently positive line bundle on the Hilbert…

math.AG2026

Some local and global properties of secant varieties of nonsingular projective curves

Lawrence Ein, Wenbo Niu, Jinhyung Park

The main goal of this paper is to study some local and global properties of secant varieties of algebraic curves. These results complement our previous work [8] by addressing issue…

math.AG2024

Effective gonality theorem on weight-one syzygies of algebraic curves

Wenbo Niu, Jinhyung Park

In 1986, Green-Lazarsfeld raised the gonality conjecture asserting that the gonality $gon (C)$ of a smooth projective curve $C$ of genus $g \geq 2$ can be read off fro…

math.AG2024

Some remarks on smooth projective varieties of small degree and codimension

Jinhyung Park

The purpose of this note is twofold. First, we give a quick proof of Ballico-Chiantini's theorem stating that a Fano or Calabi-Yau variety of dimension at least 4 in codimension tw…

math.AG2023

K-polystability of the first secant varieties of rational normal curves

In-Kyun Kim, Jinhyung Park, Joonyeong Won

The first secant variety $Σ$ of a rational normal curve of degree $d \geq 3$ is known to be a $Q$ -Fano threefold. In this paper, we prove that $Σ$ is K-polystable, and hen…

math.AG2023

A note on an effective bound for the gonality conjecture

Alexander Duncan, Wenbo Niu, Jinhyung Park

The gonality conjecture, proved by Ein--Lazarsfeld, asserts that the gonality of a nonsingular projective curve of genus $g$ can be detected from its syzygies in the embedding give…