Lorenzo Foscolo,  Sapienza.  Special Hermitian metrics on non-compact Calabi-Yau 3-folds

Martedì 27 Ottobre 2026 ore 16:00 aula 2001

Abstract: We present the construction of infinitely many examples of distinguished non-Kähler Hermitian metrics on non-compact Calabi-Yau 3-folds. These metrics solve a system of equations known as the IIB system, which arises in theoretical physics and is related to recent attempts to define notions of "canonical" metrics on non-Kähler Calabi-Yau manifolds. The examples we construct include infinitely many complete metrics obtained by deforming an asymptotically conical Kähler Ricci-flat metric in the direction of a non-trivial Äppli class and families of solutions on the ordinary double point and its smoothing that enjoy a cohomogeneity one symmetry (i.e. there is a symmetry group that acts with 1-dimensional orbit space). The talk is based on joint work with Mario Garcia-Fernandez.

Yifan Chen,  Tor Vergata.  Kähler surfaces with semipositive anticanonical bundle

Martedì 13 Ottobre 2026 ore 16:00 aula 2001

Abstract: I will discuss recent work on the classification of compact Kähler surfaces with semipositive anticanonical bundle. In particular, we prove that the blowup of projective plane at any nine points on a smooth cubic is one of them, answering a question of Demailly–Peternell–Schneider. I will explain how cylindrical geometry on a punctured neighborhood of an anticanonical elliptic curve gives a pluriharmonic function with logarithmic growth, and hence the semipositive Hermitian metric on the anticanonical bundle. This is joint work with Simion Filip, Song Sun, Valentino Tosatti, and Junsheng Zhang.