AEPPLI COHOMOLOGY CLASSES ASSOCIATED WITH GAUDUCHON METRICS ON COMPACT COMPLEX MANIFOLDS

作者：Popovici Dan^*

来源：Bulletin de la Societe Mathematique de France, 2015, 143(4): 763-800.

DOI：10.24033/bsmf.2704

• Positivity in bidegree (n-1, n-1)
• Gauduchon and sG cones
• duality between the Bott-Chern and the Aeppli cohomologies
• equation of the Monge-Ampere type in bidegree (n-1, n-1)

We propose the study of a Monge-Ampere-type equation in bidegree (n - 1, n - 1) rather than (1,1) on a compact complex manifold X of dimension n for which we prove ellipticity and uniqueness of the solution subject to positivity and normalization restrictions. Existence will hopefully be dealt with in future work. The aim is to construct a special Gauduchon metric uniquely associated with any Aeppli cohomology class of bidegree (n - 1, n - 1) lying in the Gauduchon cone of X that we hereby introduce as a subset of the real Aeppli cohomology group of type (n - 1, n - 1) and whose first properties we study. Two directions for applications of this new equation are envisaged: to moduli spaces of Calabi-Yau as partial derivative partial derivative-manifolds and to a further study of the deformation properties of the Gauduchon cone beyond those given in this paper.

• 出版日期2015