Automorphisms of irreducible holomorphic symplectic manifolds via hermitian forms (A22)

• Subject Area: Mathematics
• Term: since 2021
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 286237555

Irreducible holomorphic symplectic manifolds, also called hyperkähler manifolds, are one of the building blocks of complex manifolds with trivial first Chern class. We will classify their symmetries. Thanks to breakthroughs in the theory of hyperkähler manifolds, we can translate this geometric problem into an arithmetic one, namely, into a classification of conjugacy classes of isometries in the orthogonal group of an (indefinite) lattice. We propose to construct the isometries using hermitian forms over number fields. This yields an algorithmic approach to the classification.

• DFG Programme: CRC/Transregios
• Subproject of: TRR 195: Symbolic Tools in Mathematics and their Application
• Applicant Institution: Rheinland-Pfälzische Technische Universität Kaiserslautern-Landau
• Project Head: Professor Dr. Simon Brandhorst