- Automorphisms of irreducible holomorphic symplectic manifolds and related problems
- Billi, Simone <1996>
Subject
- MAT/03 Geometria
Description
- We study automorphisms and the mapping class group of irreducible holomorphic symplectic (IHS) manifolds. We produce two examples of manifolds of K3[2] type with a symplectic action of the alternating group A7. Our examples are realized as double EPW-sextics, the large cardinality of the group allows us to prove the irrationality of the associated families of Gushel-Mukai threefolds. We describe the group of automorphisms of double EPW-cubes. We give an answer to the Nielsen realization problem for IHS manifolds in analogy to the case of K3 surfaces, determining when a finite group of mapping classes fixes an Einstein (or Kähler-Einstein) metric. We describe, for some deformation classes, the mapping class group and its representation in second cohomology. We classify non-symplectic involutions of manifolds of OG10 type determining the possible invariant and coinvariant lattices. We study non-symplectic involutions on LSV manifolds that are geometrically induced from non-symplectic involutions on cubic fourfolds.
Date
- 2023-12-18
Type
- Doctoral Thesis
- PeerReviewed
Format
- application/pdf
Identifier
urn:nbn:it:unibo-29795
Billi, Simone (2023) Automorphisms of irreducible holomorphic symplectic manifolds and related problems, [Dissertation thesis], Alma Mater Studiorum Università di Bologna. Dottorato di ricerca in Matematica