Seminar: Paul Chemineau (G.15.25)
In this talk, we will study the $\bar{\partial}$-problem on complex surfaces with quotient singularities. This is motivated by positive results from Andersson-Lärkäng-Ruppenthal-Samuelsson-Wulcan in the context of canonical surfaces, where they used residue current theory to construct integral representation formulas. We will show how to adapt this type of proof in the context of non complete intersection spaces, to obtain such formulas for various closed extensions of the $\bar{\partial}$-operator. We will also provide a complete classification of quotient singularities for which the $\bar{\partial}$-equation is not always solvable in the $L^2$-sense.
