Degeneration of irreducible symplectic varieties

2016 Fiscal Year Final Research Report

• Project/Area Number: 26800025
• Research Category: Grant-in-Aid for Young Scientists (B)
• Allocation Type: Multi-year Fund
• Research Field: Algebra
• Research Institution: Waseda University
• Principal Investigator: NAGAI Yasunari 早稲田大学, 理工学術院, 准教授 (50572525)
• Project Period (FY): 2014-04-01 – 2017-03-31
• Keywords: 代数多様体の退化 / トーリック幾何学 / 対称群の表現

Outline of Final Research Achievements

In relation to the problem of constructing a good degeneration of irreducible symplectic manifolds, we studied the local structure of a relative Hilbert scheme associated with a semistable family of algebraic surfaces whose singular fiber has no triple point. More precisely, we clarified the structure of singularities, birational modifications and a topological invariant called orbifold cohomology of the relative symmetric product, which is given as a image of the relative Hilbert scheme under the Hilbert-Chow morphism.

Free Research Field

代数幾何学