Explore the degeneration of cubic threefolds with nodes in this comprehensive lecture by Tokio Sasaki from ICMS/IMSA. Delve into the study of smooth cubic threefolds in $\mathbb{P}^4$, examining the crucial roles of intermediate Jacobians and Fano varieties of lines in proving irrationality. Investigate the behavior of cubic threefolds with finitely many nodes, focusing on how each node determines a sextic curve and a double covering of a plane quintic curve. Learn about the isomorphism between the Jacobian of the sextic curve and the Prym variety of the quintic covering. Discover how the theory of degeneration of Prym varieties and unimodular systems of vectors as matroids can be applied to observe the limiting behavior of the Jacobian of the sextic curve based on node configurations. Gain insights from the works of A. Collino, J. P. Murre, V. Alexeev, and T. Gwena in this survey of advanced algebraic geometry concepts.
Overview
Syllabus
Degeneration of Cubic Threefolds with Nodes
Taught by
IMSA