This Valentine’s day, we will have a double bill of speakers in the geometry seminar. The speakers are Dima Panov and Nikon Kurnosov. The first talk, by Kurnosov, will be from 11-12, in the Salle de Profs. His title is “Absolutely trianalytic tori in hyperkähler manifolds”. The second talk will be 1.30-2.30, by Panov, in room O8.08. His title is “ Real line arrangements with Hirzberuch property”. Both abstracts are below.
Absolutely trianalytic tori in hyperkähler manifolds.
Let (M, g, I, J, K) be a simple hyperk\”ahler manifold, that is, a compact Riemannian manifold with holonomy equal to Sp(n). We say that a subset Z of (M, I) is trianalytic if it is complex analytic with respect to J and K, and absolutely trianalytic if it is trianalytic with respect to any hyperk\”ahler triple of complex structures (M,I,J′,K′) containing I.
I will talk about non-existence of absolutely trianalytic tori in known simple hyperk\”ahler manifolds.
Real line arrangements with Hirzberuch property.
A line arrangement of 3n lines in CP^2 satisfies the Hirzebruch property if each line intersect others in n+1 points. Hirzebruch asked if all such arrangements are related to finite complex reflection groups. We give a positive answer to this question in the case when the line arrangement in CP^2 is real, confirming that there exist exactly four such arrangements.