Ettore Lo Giudice (Universidad de Parma) impartirá la conferencia "On p-Kähler structures: AB-conjecture, and new examples"

Seminario de Geometría y Topología 

Conferencia por Ettore Lo Giudice (Universidad de Parma)

TÍTULO: On p-Kähler structures: AB-conjecture, and new examples. 

RESUMEN:
Let (M,J) be a compact complex manifold of complex dimension n. A p-Kähler structure on (M,J) is a transverse, d-closed (p,p)-form. For 1 < p < n-1, p-Kähler structures do not have a metric meaning. However, the Alessandrini-Bassanelli conjecture states that on a compact complex manifold, the existence of a p-Kähler structure implies the existence of a (p+1)-Kähler structure. Since transverse (n-1,n-1)-forms are the (n-1)-th power of the fundamental form of a Hermitian metric, then (n-1)-Kähler structures coincide with balanced metrics. Hence, a direct consequence of the Alessandrini-Bassanelli conjecture is that there exists a balanced metric on every compact p-Kähler manifold. 

In this talk, we address the Alessandrini-Bassanelli conjecture on some classes of compact complex manifolds, such as nilmanifolds equipped with a nilpotent complex structure and holomorphically parallelizable solvmanifolds. In addition to this, we discuss the existence of (n-2)-Kähler structures on complex semisimple Lie algebras of complex dimension n. The talk is based on a joint work with Asia Mainenti. 
 

Fecha: Miércoles, 17 Junio 2026 
Hora: 12:00h 
Lugar: Seminario D - Geometría y Topología, segunda planta, Edificio B