Articles
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07/02/2003--
07/02/2003
Bochner-Weitzenböck formulas and curvature actions on Riemannian manifolds
Gradients are natural first order differential operators depending on
Riemannian metrics. The principal symbols of them are related to the enveloping
algebra and higher Casimir elements. We give certain relations in the
enveloping algebra, which induce not only identities for higher Casimir
elements but also all Bochner-Weitzenb\"ock formulas for gradients. As
applications, we give some vanishing theorems.
Yasushi Homma
09/28/2005--
05/20/2004
Estimating the eigenvalues on Quaternionic Kähler Manifolds
We study geometric first order differential operators on quaternionic
K\"ahler manifolds. Their principal symbols are related to the enveloping
algebra and Casimir elements for $\Sp(1)\Sp(n)$. This observation leads to
anti-symmetry of the principal symbols and Bochner-Weitzenb\"ock formulas for
operators. As an application, we estimate the first eigenvalues of them.
Yasushi Homma
08/22/2011--
08/22/2011
Rational curves with many rational points over a finite field
We study a particular plane curve over a finite field whose normalization is
of genus 0. The number of rational points of this curve achieves the
Aubry-Perret bound for rational curves. The configuration of its rational
points and a generalization of the curve are also presented.
Satoru Fukasawa
Masaaki Homma
Seon Jeong Kim
08/25/2011--
08/25/2011
A bound on the number of points of a curve in projective space over a finite field
For a nondegenerate irreducible curve $C$ of degree $d$ in ${\Bbb P}^r$ over
${\Bbb F}_q$ with $r \geq 3$, we prove that the number $N_q(C)$ of ${\Bbb
F}_q$-points of $C$ satisfies the inequality $N_q(C) \leq (d-1)q +1$, which is
known as Sziklai's bound if $r=2$.
Masaaki Homma
04/01/2015--
04/01/2013
The characterization of Hermitian surfaces by the number of points
The nonsingular Hermitian surface of degree $\sqrt{q} +1$ is characterized by
its number of $\Bbb{F}_q$-points among the irreducible surfaces over
$\Bbb{F}_q$ of degree $\sqrt{q} +1$ in the projective 3-space.
Masaaki Homma
Seon Jeong Kim
07/22/2015--
07/22/2015
Gamma Polari-Calorimetry with SOI pixels for proposals at Extreme Light Infrastructure (ELI-NP)
We introduce the concept of Gamma Polari-Calorimetry (GPC) dedicated for
proposals at Extreme Light Infrastructure in the Romanian site (ELI-NP). A
simulation study shows that an assembly of thin SOI pixel sensors can satisfy
our requirements to GPC.
Kensuke Homma
Yoshihide Nakamiya
11/08/2016--
11/08/2016
Number of points of a nonsingular hypersurface in an odd-dimensional projective space
The numbers of $\mathbb{F}_q$-points of nonsingular hypersurfaces of a fixed
degree in an odd-dimensional projective space are investigated, and an upper
bound for them is given. Also we give the complete list of nonsingular
hypersurfaces each of which realizes the upper bound. This is a natural
generalization of our previous study of surfaces in projective $3$-space.
Masaaki Homma
Seon Jeong Kim
09/08/2015--
09/08/2015
The second largest number of points of plane curves over finite fields
A basis of the ideal of the complement of a linear subspace in a projective
space over a finite field is given. As an application, the second largest
number of points of plane curves of degree $d$ over the finite field of $q$
elements is also given for $d\geq q+1$.
Masaaki Homma
Seon Jeong Kim
03/05/2020--
03/05/2020
On a Homma-Kim conjecture for nonsingular hypersurfaces
Let $X^n$ be a nonsingular hypersurface of degree $d\geq 2$ in the projective
space $\mathbb{P}^{n+1}$ defined over a finite field $\mathbb{F}_q$ of $q$
elements. We prove a Homma-Kim conjecture on a upper bound about the number of
$\mathbb{F}_q$-points of $X^n$ for $n=3$, and for any odd integer $n\geq 5$ and
$d\leq q$.
Andrea Luigi Tironi
08/09/2016--
09/23/2014
A bound for the number of lines lying on a nonsingular surface in $3$-space over a finite field
A nonsingular surface of degree $d \geq 2$ in $\mathbb{P}^3$ over
$\mathbb{F}_q$ has at most $((d-1)q+1)d$ $\mathbb{F}_q$-lines, and this bound
is optimal for $d = 2, \sqrt{q}+1, q+1$.
Masaaki Homma
Seon Jeong Kim
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