The vanishing cycles of curves in toric surfaces : the spin case (Lionel Lang, Uppsala University)

03.04.2017 16:30 – 17:30

f the interior polygon of a lattice polygon $\Delta$ is divisible by 2, any generic curve $C$ of the linear system associated to $\Delta$ admits a spin structure $q$. If a loop in $C$ is a vanishing cycle, then the Dehn twist along the loop has to preserve $q$. As a consequence, the image of the monodromy of the linear system is a subgroup of the mapping class group $MCG(C,q)$ that preserves $q$.
The main goal of this talk is to compare the image of the monodromy with $MCG(C,q)$. To this aim, we will show on one side that $MCG(C,q)$ admits a very explicit set of generators. On the other, we will construct elements of the monodromy by tropical means. The conclusion will be that the image of the monodromy is the full group $MCG(C,q)$ if and only if the interior polygon admits no other divisors than 2.
(joint with R. Crétois)

Lieu

Bâtiment: Battelle

Séminaire "Fables géométriques"

entrée libre