11 research outputs found
Cohomological aspects on complex and symplectic manifolds
We discuss how quantitative cohomological informations could provide
qualitative properties on complex and symplectic manifolds. In particular we
focus on the Bott-Chern and the Aeppli cohomology groups in both cases, since
they represent useful tools in studying non K\"ahler geometry. We give an
overview on the comparisons among the dimensions of the cohomology groups that
can be defined and we show how we reach the -lemma
in complex geometry and the Hard-Lefschetz condition in symplectic geometry.
For more details we refer to [6] and [29].Comment: The present paper is a proceeding written on the occasion of the
"INdAM Meeting Complex and Symplectic Geometry" held in Cortona. It is going
to be published on the "Springer INdAM Series
Non-Kaehler Heterotic String Compactifications with non-zero fluxes and constant dilaton
We construct new explicit compact supersymmetric valid solutions with
non-zero field strength, non-flat instanton and constant dilaton to the
heterotic equations of motion in dimension six. We present balanced Hermitian
structures on compact nilmanifolds in dimension six satisfying the heterotic
supersymmetry equations with non-zero flux, non-flat instanton and constant
dilaton which obey the three-form Bianchi identity with curvature term taken
with respect to either the Levi-Civita, the (+)-connection or the Chern
connection. Among them, all our solutions with respect to the (+)-connection on
the compact nilmanifold satisfy the heterotic equations of motion.Comment: LaTeX, 16 pp., no figures, new Theorem 1.1, references adde
Stability of strongly Gauduchon manifolds under modifications
International audienc
Deformation limits of projective manifolds : Hodge numbers and strongly Gauduchon metrics
International audienc