2017 Fiscal Year Research-status Report
On Generalized Pure Braid Groups
| Project/Area Number |
16K05051
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| Research Institution | Hokkaido University |
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Principal Investigator |
セッテパネーラ シモーナ 北海道大学, 理学研究院, 准教授 (40721890)
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| Project Period (FY) |
2016-04-01 – 2019-03-31
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| Keywords | Discriminantal arrang. / braid groups / Grassmannian / Plucker embedding / fundamental groups / Pappus's theorem |
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| Outline of Annual Research Achievements |
During this year of research the Principal Investigator (P.I.) worked to the project with A. Libgober and completed two papers Discriminantal Arrangement, 3 x 3 Minors of Plucker Matrix and hypersurfaces in Grassmannian Gr(3,n) and Pappus"s Theorem in Grassmannian Gr(3,n) with her students S. Sawada and S. Yamagata. The first already published, the second submitted.
In those papers the result obtained in the paper with A. Libgober is connected to the study of hypersurfaces in Grassmannian, showing that special conbinatorics property of intersection lattice of Discriminantal arrangements describe hypersurfaces in the Grassmannian when view as projective variety. Moreover it has been possible to finally give a conjecture on the complete intersection lattice of Discriminantal arrangement obtaining also some partial results on combinatorics of higher strata of Dicsriminantal arrangement.
Moreover the P.I. finished a paper with a second co-author, M. Torielli.
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| Current Status of Research Progress |
Current Status of Research Progress
2: Research has progressed on the whole more than it was originally planned.
Reason
The project started with the idea of study higher dimensional Braid groups, proved to be much more interesting than expe
cted. Indeed it turned out to be related to several very important mathematical objects both in combinatorics and algebraic geometry. Indeed the research lead to the study of the combinatorics of Discriminantal arrangement that is a whidely
studied object in algebra, in combinatorics and in algebraic geometry. The results obtained in the project allowed to finally make a conjecture on the complete description of intersection lattice of Discriminantal arrangement. The P.I. jointly with his co-researcher A. Libgober and her students has been able to prove some partial result toward the final proof of the conjecture.
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| Strategy for Future Research Activity |
The future research of the P.I. will mainly focus on the proof of conjecture about intersection lattice of Discriminantal arrangement. In particular to generalize the result they got on the existence of m-strata of multimplicity m+1. Moreover she wants to investigate possible connections between very non generic configurations of points in projective space and special combinatorics for Discriminantal arrangement. Moreover the P.I. is planning to continue studies with P. Bailet that already lead to a paper accepted for publication
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| Causes of Carryover |
The amount is only 5008 yen destinated to buy a needed book for next fiscal year.
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