8 citations · 24 across the 9 of their papers we have counts for
9 papers
The Strong Lefschetz Property of Gorenstein Algebras Generated by Relative Invariants
Takahiro Nagaoka, Akihito Wachi
We prove the strong Lefschetz property for Artinian Gorenstein algebras generated by the relative invariants of prehomogeneous vector spaces of commutative parabolic type.
Strictness of the log-concavity of generating polynomials of matroids
Satoshi Murai, Takahiro Nagaoka, Akiko Yazawa
Recently, it was proved by Anari-Oveis Gharan-Vinzant, Anari-Liu-Oveis Gharan-Vinzant and Brändén-Huh that, for any matroid , its basis generating polynomial and its independent…
An additive basis for the cohomology rings of regular nilpotent Hessenberg varieties
Makoto Enokizono, Tatsuya Horiguchi, Takahiro Nagaoka +1
In this paper we construct an additive basis for the cohomology ring of a regular nilpotent Hessenberg variety which is obtained by extending all Poincaré duals of smaller regular…
Uniform bases for ideal arrangements
Makoto Enokizono, Tatsuya Horiguchi, Takahiro Nagaoka +1
In this paper we introduce and study uniform bases for the ideal arrangements in all Lie types. Explicit uniform bases are given by Abe-Horiguchi-Masuda-Murai-Sato for types $A,B,C…
The universal covers of hypertoric varieties and Bogomolov's decomposition
Takahiro Nagaoka
In this paper, we study the (singular) universal cover of an affine hypertoric variety. We show that it is given by another affine hypertoric variety, and taking the universal cove…
Strict log-concavity of the Kirchhoff polynomial and its applications to the strong Lefschetz property
Takahiro Nagaoka, Akiko Yazawa
Anari, Gharan, and Vinzant proved (complete) log-concavity of the basis generating functions for all matroids. From the viewpoint of combinatorial Hodge theory, it is natural to as…
The universal Poisson deformation of hypertoric varieties and some classification results
Takahiro Nagaoka
In this paper, we study and describe the universal Poisson deformation space of hypertoric varieties concretely. In the first application, we show that affine hypertoric varieties…
On a sufficient condition for a Fano manifold to be covered by rational -folds
Takahiro Nagaoka
In this paper, we prove a conjecture by T. Suzuki, which says if a smooth Fano manifold satisfies some positivity condition on its Chern character, then it can be covered by ration…
Reflexive polytopes arising from edge polytopes
Takahiro Nagaoka, Akiyoshi Tsuchiya
It is known that every lattice polytope is unimodularly equivalent to a face of some reflexive polytope. A stronger question is to ask whether every -polytope is unimodularl…