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Abstract: In this talk, we will discuss the boundedness of Calabi-Yau threefolds admitting an elliptic fibration. First, we will review the notion of boundedness in birational geometry and its weak forms. Then, we will switch focus to Calabi-Yau varieties and discuss how the Kawamata-Morrison cone conjecture comes in the picture when studying boundedness properties for this class of varieties. To conclude, we will see how this circle of ideas applies to the case of elliptic Calabi-Yau threefolds. This talk is based on work joint with C.D. Hacon and R. Svaldi. |
