In 1978 Yau (Yau, 1978) confirmed a conjecture due to Calabi (1954) stating the existence of Kähler metrics with prescribed Ricci forms on compact Kähler manifolds. A version of this statement for effective orbifolds can be found in the literature (Joyce, 2000; Boyer and Galicki, 2008; Demailly and Kollár, 2001). In this expository article, we provide details for a proof of this orbifold version of the statement by adapting Yau’s original continuity method to the setting of effective orbifolds in order to solve a Monge–Ampère equation. We then outline how to obtain Kähler–Einstein metrics on orbifolds with negative first Chern class by solving a slightly different Monge–Ampère equation. We conclude by listing some explicit examples of Calabi–Yau orbifolds, which consequently admit Ricci flat metrics by Yau’s theorem for effective orbifolds.

1978年，丘（Yau，1978）证实了一个猜想，这是由于卡拉比（Calabi，1954）指出了紧致Kähler流形上具有规定Ricci形式的Kähler度量的存在。在文献中可以找到关于有效球架的这种说法的一个版本（Joyce，2000； Boyer和Galicki，2008； Demailly和Kollár，2001）。在此说明性文章中，我们通过调整丘（Yau）的原始连续性方法来设置有效有效单数以解决Monge–Ampère方程，来详细说明该语句的适时形式。然后，我们概述了如何通过求解稍有不同的Monge-Ampère方程来获得第一类Chern类为负的球面上的Kähler-Einstein度量。最后，我们列出了一些关于Calabi–Yau双折的显式示例，这些示例因此根据有效定圆的丘定理接受Ricci平面度量。