The International Center for Mathematical Sciences – Sofia (ICMS-Sofia)
The Institute of the Mathematical Sciences of the Americas (IMSA-Miami)


Joint ICMS & IMSA Seminar

January 21, 2022,
09:30 AM Eastern Time (US and Canada)

Hosted by IMSA-Miami, via Zoom

Tokio Sasaki


Degeneration of Cubic threefolds with nodes

For a general smooth cubic threefolds $X$ in $\mathbb{P}^4$, its intermediate Jacobian and the fano variety of lines play the main role in the proof of the irrationality of $X$. When $X$ is a cubic with finitely many nodes, each node determines a sextic curve and a double covering of plane quintic curve similarly as smooth cubics. Since the Jacobian of the former curve is isomorphic to the Prym variety of the latter covering, by applying the theory of degeneration of Prym varieties and unimodular systems of vectors as matroids, one can observe the limiting behaviour of the Jacobian of the sextic curve from the configuration of nodes. This is a survey talk mainly based on results by A. Collino, J. P. Murre, V. Alexeev, and T. Gwena.

Тhe seminar will be held via Zoom.