Page 117 - 8th European Congress of Mathematics ∙ 20-26 June 2021 ∙ Portorož, Slovenia ∙ Book of Abstracts
P. 117
TOPICS IN COMPLEX AND QUATERNIONIC GEOMETRY (MS-74)
On cohomogeneity one Hermitian non-Kähler manifolds
Daniele Angella, daniele.angella@unifi.it
Università di Firenze, Italy
Coauthor: Francesco Pediconi
We study Hermitian manifolds with a compact Lie group action by holomorphic isometries with
principal orbits of codimension one. In particular, we focus on a special class of these manifolds
constructed by following Bérard-Bergery, which includes, among the others, the holomorphic
line bundles on CP m−1, the linear Hopf manifolds and the Hirzebruch surfaces. We character-
ize their invariant special Hermitian metrics, such as balanced, Kähler-like, pluriclosed, locally
conformally Kähler, Vaisman, Gauduchon. Furthermore, we construct new examples of coho-
mogeneity one Hermitian metrics solving the second-Chern-Einstein equation and the constant
Chern-scalar curvature equation.
Slice Regular Quaternionic Manifolds.
Cinzia Bisi, bsicnz@unife.it
Ferrara University, Italy
Coauthors: Graziano Gentili, Daniele Angella
In recent years, Slice Regular Quaternionic Manifolds have been introduced and studied by
many authors, after the seminal definition of Slice Regular Function given by G. Gentili and
D.C. Struppa in 2006-2007.
Slice Regular Quaternionic Manifolds have catched the attention because they have more struc-
ture than the real ones but they are less docile than the complex ones, due to the lack of com-
mutativity in the product of two quaternionic numbers.
In this talk we will focus mainly on the two following examples:
1) Quaternionic Tori , their slice regular automorphisms group and their Moduli Space;
2) Quaternionic Hopf Surfaces , their slice regular automorphisms group and their deforma-
tions.
In both cases we will present the state of the art results and also some open problems.
Symplectic duality and implosion
Andrew Dancer, dancer@maths.ox.ac.uk
Oxford University, United Kingdom
We discuss symplectic duality between hyperkahler spaces and present candidates for the sym-
plectic duals of various hyperkahler implosion spaces. (Joint work with A.Hanany, F.Kirwan,
A.Bourget, Z.Zhong,J.Grimminger)
115
On cohomogeneity one Hermitian non-Kähler manifolds
Daniele Angella, daniele.angella@unifi.it
Università di Firenze, Italy
Coauthor: Francesco Pediconi
We study Hermitian manifolds with a compact Lie group action by holomorphic isometries with
principal orbits of codimension one. In particular, we focus on a special class of these manifolds
constructed by following Bérard-Bergery, which includes, among the others, the holomorphic
line bundles on CP m−1, the linear Hopf manifolds and the Hirzebruch surfaces. We character-
ize their invariant special Hermitian metrics, such as balanced, Kähler-like, pluriclosed, locally
conformally Kähler, Vaisman, Gauduchon. Furthermore, we construct new examples of coho-
mogeneity one Hermitian metrics solving the second-Chern-Einstein equation and the constant
Chern-scalar curvature equation.
Slice Regular Quaternionic Manifolds.
Cinzia Bisi, bsicnz@unife.it
Ferrara University, Italy
Coauthors: Graziano Gentili, Daniele Angella
In recent years, Slice Regular Quaternionic Manifolds have been introduced and studied by
many authors, after the seminal definition of Slice Regular Function given by G. Gentili and
D.C. Struppa in 2006-2007.
Slice Regular Quaternionic Manifolds have catched the attention because they have more struc-
ture than the real ones but they are less docile than the complex ones, due to the lack of com-
mutativity in the product of two quaternionic numbers.
In this talk we will focus mainly on the two following examples:
1) Quaternionic Tori , their slice regular automorphisms group and their Moduli Space;
2) Quaternionic Hopf Surfaces , their slice regular automorphisms group and their deforma-
tions.
In both cases we will present the state of the art results and also some open problems.
Symplectic duality and implosion
Andrew Dancer, dancer@maths.ox.ac.uk
Oxford University, United Kingdom
We discuss symplectic duality between hyperkahler spaces and present candidates for the sym-
plectic duals of various hyperkahler implosion spaces. (Joint work with A.Hanany, F.Kirwan,
A.Bourget, Z.Zhong,J.Grimminger)
115
