Speaker: Sergey Galkin

Title: Branched covers and the explanation for miraculous "Golyshev-Mendeleev’s table"

Date: Apr 6, 2015, 16:15

Place: Séminaire de Géométrie Tropicale, Institut Mathématiques de Jussieu, Université Pierre et Marie Curie, Paris 6, salle 1525-502

Abstract:

Ten years ago Golyshev proposed to classify the families of Fano threefolds of first kind
by two integer invariants: Fano index r and a the so-called level N.
Then the generating series (G-series) counting rational curves on these threefolds
can be expressed by a uniform formula that depends only on r and N.
He also noticed that for reason unknown the G-series for varieties sharing same level
are related by a change of coordinate t to t^r.
In joint work with Tom Coates using a theorem of Jeff Brown we prove
that when one variety is a cyclic cover of another branched in subcanonical divisor,
then their G-series are related by the change of coordinates above.
Since special members in the families of Fano threefolds of the same level
are the respective branched covers, this gives and explanation to the observation of Golyshev.