21 citations · 51 across the 10 of their papers we have counts for
13 papers
On the prime ideals of higher secant varieties of Veronese embeddings of small degrees
Katsuhisa Furukawa, Kangjin Han
In this paper, we study minimal generators of the (saturated) defining ideal of the -secant variety of the image of the -uple Veronese embedding $v_d…
Sullivant-Talaska ideal of the cyclic Gaussian Graphical Model
Austin Conner, Kangjin Han, Mateusz Michałek
In this paper, we settle a conjecture due to Sturmfels and Uhler concerning generation of the prime ideal of the variety associated to the Gaussian graphical model of any cycle gra…
A family of explicit Waring decompositions of a polynomial
Kangjin Han, Hyunsuk Moon
In this paper we settle some polynomial identity which provides a family of explicit Waring decompositions of any monomial over a field …
On the singular loci of higher secant varieties of Veronese embeddings
Katsuhisa Furukawa, Kangjin Han
The -th secant variety of a projective variety , denoted by , is defined to be the closure of the union of -planes spanned by points o…
A new bound for the Real Waring rank of monomials
Kangjin Han, Hyunsuk Moon
In this paper we consider the Waring rank of monomials over the real and the rational numbers. We give a new upper bound for it by establishing a way in which one can take a struct…
On the first non-trivial strand of syzygies of projective schemes and Condition
Jeaman Ahn, Kangjin Han, Sijong Kwak
Let be any -dimensional closed subscheme. We are mainly interested in two notions related to syzygies: one is the property $\mathbf{N}_{d,p}~(d\ge 2,…
Rank 3 Quadratic Generators of Veronese Embeddings
Kangjin Han, Wanseok Lee, Hyunsuk Moon +1
Let be a very ample line bundle on a projective scheme defined over an algebraically closed field with . We say that satisfies prop…
On the locus of points of high rank
Jarosław Buczyński, Kangjin Han, Massimiliano Mella +1
Given a closed subvariety X in a projective space, the rank with respect to X of a point p in this projective space is the least integer r such that p lies in the linear span of so…
On singularities of third secant varieties of Veronese embeddings
Kangjin Han
In this paper we study singularities of third secant varieties of Veronese embedding , which corresponds to the variety of symmetric tensors of border rank at mo…
Linear normality of general linear sections and some graded Betti numbers of 3-regular projective schemes
Jeaman Ahn, Kangjin Han
In this paper we study graded Betti numbers of any nondegenerate 3-regular algebraic set in a projective space . More concretely, via Generic initial ideals (Gin…
Sharp bounds for higher linear syzygies and classifications of projective varieties
Kangjin Han, Sijong Kwak
In the present paper, we consider upper bounds of higher linear syzygies i.e. graded Betti numbers in the first linear strand of the minimal free resolutions of projective varietie…
Classification of secant defective manifolds near the extremal case
Kangjin Han
Let be a nondegenerate irreducible closed subvariety of dimension over the field of complex numbers and let be its secant variety. i…
Analysis on some infinite modules, inner projection, and applications
Kangjin Han, Sijong Kwak
A projective scheme is called `quadratic' if is scheme-theoretically cut out by homogeneous equations of degree 2. Furthermore, we say satisfies `property $\textbf{N}_{…