Feix-Kaledin Metric on the Total Spaces of Cotangent Bundles to Kähler Quotients

Student: Abasheva Anna

Educational Programme: Mathematics (Bachelor)

Final Grade: 10

Year of Graduation: 2020

In this paper we study the geometry of the total space Y of a cotangent bundle to a Kähler manifold N obtained as a Kähler reduction from C^n. Using the hyperkähler reduction we construct a hyperkähler metric on Y and prove that it coincides with the canonical Feix——Kaledin metric. This metric is in general non-complete. We show that the metric completion \tilde Y of the space Y is equipped with a structure of a stratified hyperkähler space. Pick a complex structure J on \tilde Y induced from quaternions. Suppose that J is neither I nor -I where I is the complex structure whose restriction to Y = T*N is induced by the complex structure on N. We prove that the space \tilde Y_J admits an algebraic structure and is an affine variety.

Full text (added May 29, 2020)

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