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Speaker: Rikuto Ito

Affiliation: Nagoya University

Title: Rigid Calabi–Yau Threefolds and Their Intermediate Jacobians

Abstract: 
For every complex threefold X, one can associate the intermediate Jacobian J^2(X), which is a complex torus. This invariant plays a fundamental role in the study of the geometry of threefolds. However, since the construction of J^2(X) is highly analytic in nature, it is an important problem to find an algebraic description of it.

When X is a rigid Calabi-Yau threefold, the intermediate Jacobian J^2(X) is an elliptic curve. Even in this case, an algebraic construction of J^2(X) is not yet fully understood except in certain special examples. M. Saito and N. Yui have suggested the question of whether a rigid Calabi–Yau threefold X has a model defined over \mathbb{Q} if and only if its intermediate Jacobian J^2(X) does.

In this talk, we will reformulate this question in terms of the period map for rigid Calabi-Yau threefolds and outline the steps toward a proof. This is joint work with Noriko Yui.