5 citations · 10 across the 11 of their papers we have counts for
12 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…
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…
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…
On separable higher Gauss maps
Katsuhisa Furukawa, Atsushi Ito
We study the -th Gauss map in the sense of F.~L.~Zak of a projective variety over an algebraically closed field in any characteristic. For all integer $…
Dimension of the space of conics on Fano hypersurfaces
Katsuhisa Furukawa
R. Beheshti showed that, for a smooth Fano hypersurface of degree over the complex number field , the dimension of the space of lines lying in is equal…
A combinatorial description of dual defects of toric varieties
Katsuhisa Furukawa, Atsushi Ito
From a finite set in a lattice, we can define a toric variety embedded in a projective space. In this paper, we give a combinatorial description of the dual defect of the toric var…
On Gauss maps in positive characteristic in view of images, fibers, and field extensions
Katsuhisa Furukawa, Atsushi Ito
The Gauss map of a projective variety is a rational map from to a Grassmann variety. In positive characteristic, we show the following results. (1) For…
Gauss maps of toric varieties
Katsuhisa Furukawa, Atsushi Ito
We investigate Gauss maps of (not necessarily normal) projective toric varieties over an algebraically closed field of arbitrary characteristic. The main results are as follows: (1…
Convex separably rationally connected complete intersections
Katsuhisa Furukawa
We give a generalization of a result of R. Pandharipande to arbitrary characteristic: We prove that, if is a convex, separably rationally connected, smooth complete intersectio…
On general fibers of Gauss maps in positive characteristic
Katsuhisa Furukawa
A general fiber of the Gauss map of a projective variety in coincides with a linear subvariety of in characteristic zero. In positive characteristic,…
Cohomological characterization of hyperquadrics of odd dimensions in characteristic two
Katsuhisa Furukawa
We consider characterizations of projective varieties in terms of their tangents. S. Mori established the characterization of projective spaces in arbitrary characteristic by ample…
Duality with expanding maps and shrinking maps, and its applications to Gauss maps
Katsuhisa Furukawa
We study expanding maps and shrinking maps of subvarieties of Grassmann varieties in arbitrary characteristic. The shrinking map was studied independently by Landsberg and Piontkow…