An extension of the Gudkov--Rokhlin congruence to singular curves

Abstract: Joint work in progress w/ Ilia Itenberg.

Upon completing the deformation classification of simple real plane sextic curves with smooth real part, we observed certain distinctive lacunas in our list of topological types. These lacunas are very similar to those in the smooth case, which originally led to the discovery of the Gudkov--Rokhlin congruence. However, ours depend on the set of singularities and, therefore, need a new dedicated congruence; we suggest one.

A remarkable fact supported by our classification and explained in the proof is that the congruence holds for *many*, but not *all* types of singularities. In particular, simple nodes (that would normally serve as a litmus test for any singularity related statement) are excluded!

In spite of the algebra-geometric setting, the proof is mostly topological.

algebraic geometry

Audience: researchers in the discipline

ODTU-Bilkent Algebraic Geometry Seminars