Zobrazeno 1 - 10
of 141
pro vyhledávání: '"Park, Euisung"'
Autor:
Park, Euisung, Sim, Saerom
This paper studies the geometric structure of the locus $\Phi_3 (X)$ of rank $3$ quadratic equations of the Veronese variety $X = \nu_d (\mathbb{P}^n)$. Specifically, we investigate the minimal irreducible decomposition of $\Phi_3 (X)$ of rank $3$ qu
Externí odkaz:
http://arxiv.org/abs/2412.16983
Autor:
Lee, Donghyeop, Park, Euisung
Let $\Gamma \subset \mathbb{P}^n$ be a nondegenerate finite subscheme of degree $d$. Then the Castelnuovo-Mumford regularity ${\rm reg} ({\Gamma})$ of $\Gamma$ is at most $\left\lceil \frac{d-n-1}{t(\Gamma)} \right\rceil +2$ where $t(\Gamma)$ is the
Externí odkaz:
http://arxiv.org/abs/2412.15096
In this article, we investigate the rank index of projective curves $\mathscr{C} \subset \mathbb{P}^r$ of degree $r+1$ when $\mathscr{C} = \pi_p (\tilde{\mathscr{C}})$ for the standard rational normal curve $\tilde{\mathscr{C}} \subset \mathbb{P}^{r+
Externí odkaz:
http://arxiv.org/abs/2411.17494
Let $X$ be a non-degenerate projective irreducible variety of dimension $n \ge 1$, degree $d$, and codimension $e \ge 2$ over an algebraically closed field $\mathbb{K}$ of characteristic $0$. Let $\beta_{p,q} (X)$ be the $(p,q)$-th graded Betti numbe
Externí odkaz:
http://arxiv.org/abs/2404.03293
Autor:
Park, Euisung
Let $X \subset \P^r$ be a linearly normal variety defined by a very ample line bundle $L$ on a projective variety $X$. Recently it is shown in \cite{HLMP} that there are many cases where $(X,L)$ satisfies property $\textsf{QR} (3)$ in the sense that
Externí odkaz:
http://arxiv.org/abs/2208.12481
Autor:
Moon, Hyunsuk, Park, Euisung
Regarding the generating structure of the homogeneous ideal of a projective variety $X \subset \mathbb{P}^r$, we define the rank index of $X$ to be the smallest integer $k$ such that $I(X)$ can be generated by quadratic polynomials of rank at most $k
Externí odkaz:
http://arxiv.org/abs/2206.08586
Autor:
Park, Euisung
Let $\mathcal{C} \subset \mathbb{P}^r$ be a linearly normal curve of arithmetic genus $g$ and degree $d$. In \cite{SD}, B. Saint-Donat proved that the homogeneous ideal $I(\mathcal{C})$ of $\mathcal{C}$ is generated by quadratic equations of rank at
Externí odkaz:
http://arxiv.org/abs/2202.00857
Autor:
Jung, Jaeheun, Park, Euisung
The study of the defining equations of a finite set $\Gamma \subset \mathbb{P}^n$ in linearly general position has been actively attracted since it plays a significant role in understanding the defining equations of arithmetically Cohen-Macaulay vari
Externí odkaz:
http://arxiv.org/abs/2007.06893
Publikováno v:
Compositio Math.157 (2021), no. 9, 2001-2025
Let $L$ be a very ample line bundle on a projective scheme $X$ defined over an algebraically closed field $\Bbbk$ with ${\rm char}~\Bbbk \neq 2$. We say that $(X,L)$ satisfies property $\mathsf{QR}(k)$ if the homogeneous ideal of the linearly normal
Externí odkaz:
http://arxiv.org/abs/2001.06687
Publikováno v:
In Journal of Algebra 15 December 2023 636:732-756
