Cech coboundary equations on a certain class of nodal curves

by Jinichiro Tanaka (Osaka Metropolitan U.)

Tuesday Oct 8, 2024, 11:00 AM → 12:00 PM Europe/Paris

salle de conférence (LJAD)

Let $C$ be a compact complex curve holomorphically embedded in a non-singular complex surface $S$.

When the normal line bundle $N_{C/S} := [C] |_C$ is negative (resp. positive), $C$ has a neighborhood (resp. a fundamental system of neighborhoods)  with pseudoconvexity (resp. pseudoconcavity) , which is a complex analogue of the convexity (resp. concavity).

What if $N_{C/S}$ is flat ?

Assume that $C$ has only one node and $N_{C/S}$ is flat.

Under the assumption, Koike showed that the analytic structure of a neighborhood of $C$ is determined by some irrational theoretical number condition.

In this talk, we construct a compact complex curve $C$ as above which satisfies the assumption and observe cohomology of a neighborhood of $C$.

This is a joint work with Satoshi Ogawa.