Canonical sheaves at isolated canonical singularities

Abstract: The canonical line bundle and the corresponding canonical sheaf belong to the most important geometric/analytic objects associated to a complex manifold. They play a crucial role e.g. in classification theory, Serre duality or vanishing theorems. If we consider singular varieties instead of smooth manifolds, then there exist various possibilities to generalize the canonical sheaf to that setting. One can consider for example the Grothendieck(-Barlet-Henkin-Passare) dualizing sheaf or the Grauert-Riemenschneider L2-sheaf. In this talk, we will discuss another possible generalization, i.e., the sheaf of L2 holomorphic n-forms with a certain boundary condition at the singular set. This sheaf is essential for L2-dbar-theory on singular spaces, but difficult to understand. We will describe it explicitly for isolated canonical Gorenstein singularities.

algebraic geometryalgebraic topologycomplex variablesdifferential geometrygeometric topologymetric geometryquantum algebrarepresentation theory

Audience: researchers in the topic

Sapienza A&G Seminar

Series comments: Weekly research seminar in algebra and geometry.

"Sapienza" Università di Roma, Department of Mathematics "Guido Castelnuovo".