2019 Fiscal Year Final Research Report
Moduli of sheaves on a cubic fourfold and irreducible symplectic manifolds
| Project/Area Number |
17K05212
|
|---|
| Research Category |
Grant-in-Aid for Scientific Research (C)
|
| Allocation Type | Multi-year Fund |
|---|
| Section | 一般 |
|---|
| Research Field |
Algebra
|
|---|
| Research Institution | Waseda University |
|---|
Principal Investigator |
|
|---|
| Project Period (FY) |
2017-04-01 – 2020-03-31
|
| Keywords | 代数幾何学 |
|---|
| Outline of Final Research Achievements |
We studied the irreducible component of the moduli space of stable sheaves on a cubic fourfold with the Hilbert polynomial 5n+2 that contains O(1) of a ratinoal normal quintic curve, and aimed at constructing explicitly the space of sheaves or complexes that are given by a Kuznetsov projection of the original sheaves. The key in constructing such a space is hidden in the locus of stable sheaves that are supported on a cubic surface given by a linear section of the original cubic fourfold. We found that the moduli of such sheaves can be described by a GIT quotient in relation to a certain moduli space of quiver representations.
|
| Free Research Field |
代数幾何学
|
| Academic Significance and Societal Importance of the Research Achievements |
近年，代数多様体の導来圏の対象をパラメータ付けするモジュライ空間の研究が，代数幾何学の分野のみならず，数理物理の動機づけもあって非常に盛んであるが，この研究で構成しようと試みているモジュライ空間もこの種のものの非常に具体的な例である．科研費の期間中に求めるモジュライ空間の完全な記述までたどり着くことはできなかったが，本研究のアプローチは極めて明示的であり，抽象的である種漠然とした導来圏の安定性条件と安定対象のモジュライ空間について古典的かつ明示的な説明を与えるものとなり，高い学術的な意義を持つ．
|
