Kähler-Einstein metrics on Kummer threefold and special Lagrangian tori (Q1818728)

Deformations of Calabi-Yau metrics on a Kummer threefold \(Y\) are studied using as main tool the deformations of special Lagrangian tori on \(Y\). Here \(Y\) is obtained as the minimal resolution of the quotient \(Y_0\) of the product of three elliptic curves by a diagonal \({\mathbb Z}_3\)-action. By gluing the complete Calabi metric on each of the neighbourhoods of the exceptional fibers to the background flat metric the author shows that there are approximate Calabi-Yau metrics on \(Y\), a phenomenon previously studied for the \(K_3\) surface in [\textit{R. Kobayashi}, Adv. Stud. Pure Math. 18, No. 2, 257-311 (1990; Zbl 0755.32023)].