Katsuhisa Furukawa

activity

20172024

collaborators

5 papers

math.AG2024

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 $k$ -secant variety $σ_{k} (v_{d} (P^{n}))$ of the image of the $d$ -uple Veronese embedding $v_d…

math.AG2021

On the singular loci of higher secant varieties of Veronese embeddings

Katsuhisa Furukawa, Kangjin Han

The $k$ -th secant variety of a projective variety $X \subset P^{N}$ , denoted by $σ_{k} (X)$ , is defined to be the closure of the union of $(k - 1)$ -planes spanned by $k$ points o…

math.AG2018

Cubic hypersurfaces with positive dual defects

Katsuhisa Furukawa

We show that if a cubic hypersurface with positive dual defect over the complex number field is not a cone, then either the hypersurface coincides with the secant variety of the si…

math.AG2017

On separable higher Gauss maps

Katsuhisa Furukawa, Atsushi Ito

We study the $m$ -th Gauss map in the sense of F.~L.~Zak of a projective variety $X \subset P^{N}$ over an algebraically closed field in any characteristic. For all integer $…

math.AG2017

Dimension of the space of conics on Fano hypersurfaces

Katsuhisa Furukawa

R. Beheshti showed that, for a smooth Fano hypersurface $X$ of degree $\leq 8$ over the complex number field $C$ , the dimension of the space of lines lying in $X$ is equal…