| Project/Area Number |
16K05051
|
|---|
| Research Category |
Grant-in-Aid for Scientific Research (C)
|
| Allocation Type | Multi-year Fund |
|---|
| Section | 一般 |
|---|
| Research Field |
Algebra
|
|---|
| Research Institution | Hokkaido University |
|---|
Principal Investigator |
|
|---|
| Research Collaborator |
Libgober Anatoly
Sawada Sumire
Yamagata So
Bailet Pauline
Guerville-Balle Benoit
|
|---|
| Project Period (FY) |
2016-04-01 – 2019-03-31
|
| Project Status |
Completed (Fiscal Year 2018)
|
| Budget Amount *help |
¥4,290,000 (Direct Cost: ¥3,300,000、Indirect Cost: ¥990,000)
Fiscal Year 2018: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
Fiscal Year 2017: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
Fiscal Year 2016: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
|
|---|
| Keywords | Discriminantal Arrang. / Bruhat Orders / Braid Groups / Discriminantal Arrang / Higher Bruhat Orders / Discriminantal arrang. / braid groups / Grassmannian / Plucker embedding / fundamental groups / Pappus's theorem / Gale transform / 代数学 / 配置空間 / 組紐群 / 超平面配置 / 基本群 |
|---|
| Outline of Final Research Achievements |
Manin Schechtmann arrangements MS(n,k) are defined as the set of parallel translates of a given arrangement of n hyperplanes in a k-space which fail to form a general position arrangement. We studied the First topological invariants of MS(n,k), we found generating function that gives Asymptotic behaviour of the Betti numbers and chambers of MS(n,k). Moreover we proved that the number of chambers on MS(n,k) is a lower bound for the number of elements in the set of Bruhat orders B(n,k) and studied freeness of MS(k+3,k).If the arrangement A is generic enough then the intersection lattice of MS(n,k,A) is independent of A. Such arrangements are called very generic arrangements, and then the Manin-Schechtmann arrangements are noted MS(n,k). In this particular case, the intersection lattice of MS(n,k) have been explicitly described by Athanasiadis.
Using similar arguments as in a paper of Salvetti and Settepanella, we give description of betti numbers of MS(n,k).
|
| Academic Significance and Societal Importance of the Research Achievements |
We studied the topological invariants of the Manin Schechtmann arrangements MS(n,k,A) in non very generic case. This provided a way to study the difficult problem of special configurations of points in the projective space, one of the main problems in phisics and geometry, using combinatorics.
|
