Geometria Complessa e Geometria Differenziale
Geometria Complessa e Geometria Differenziale
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Projective HK manifolds have finitely many real structures

Andrea Cattaneo (Università degli Studi di Parma)

created by daniele on 16 May 2019
modified on 21 Jun 2019

27 jun 2019 -- 14:30

Aula Tricerri, DiMaI, Firenze

Abstract.

One of the problems lying on the boundary berween complex and real geometry is the classification of the so called real structures on a given manifold. Given a complex manifold, a real structure is nothing but an an anti-holomorphic diffeomorphism of order two of the underlying real manifold, which plays the role of complex conjugation. The fixed locus of such an involution is called a real form of the manifold, and in fact we can recover our original manifold by extension of scalars from any of its real forms. Of course, a manifold can have pairwise non-isomorphic real forms and the first problem is to decide wether there are only finitely many of them. The answer to this question is known in low dimension, i.e., for curves and surfaces, and in this talk we will provide an answer in the case where the manifold under consideration is hyperkähler, showing the finiteness (up to isomorphism) of the number of real forms in this case.

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