Affiliation: Joint Graduate School of Mathematics for Innovation, Kyushu University, Fukuoka, Japan
E-mail: maehara.shota.027 "at" s.kyushu-u.ac.jp
Key words: Hyperplane arrangement; Multiarrangement; Logarithmic derivation module; Extendability; Chamber of arrangements
(Exponents of the Coxeter multiarrangement of type B_2)
Let us consider multiarrangements in a 2-dimensional vector space over a field of characteristic zero.
For 2-dimensional multiarrangements, the exponenets of them are very important to consider the freeness of 3-dimensional simple arrangements.
Now I'm wondering if we can completely solve the exponents for multiarrangements of the Coxeter arrangment of type B_2,
which is the line arrangement defined by xy(x-y)(x+y).
(Minimum number of chambers)
When we arrange a finite set of lines into a 2-dimensional real vector space,
the complement of lines can be considered as a division of the plane. Let us call the maximal connected components chambers.
It is well known that the number of chambers becomes maximum when all intersection points are double points.
However, to determine the arrangement which gives the minimum number is much more difficult. A very famous theorem in the theory of hyperplane arrangement,
called Yoshinaga's criterion, gives a lower bound of chambers in an algebraic way.
I am interested in the gap between the lower bound obtained from Yoshinaga's criterion and the minimum number in real.
November 1998: Born in Hamada city, Shimane prefecture, Japan
April 2017--March 2021: Bachelor of Engineering Degree, Kyushu University
April 2022--March 2024: Master of Mathematics Degree, Kyushu University
April 2024--: Ph.D. student in Kyushu University