The Hodge-Deligne polynomials of some moduli spaces of coherent systems
Vortrag von Dr. Matteo Tommasini
Sprecher eingeladen von: Prof. Dr. Joseph Ayoub
Datum: 30.05.12 Zeit: 11.30 - 12.15 Raum: Y27H12
A coherent system on a smooth curve C consists of a pair (E,V) where E is a vector bundle on C (of rank n and degree d) and V is a subspace (of dimension k) of $H^0(E)$. For each triple (n,d,k) there is a family of moduli spaces depending on a real positive parameter $\alpha$. It is known that these moduli spaces change only if we pass through a finite set of critical values, so we have a finite number of distinct moduli spaces labeled according to the corresponding interval in the real line. The final moduli space is in general very simple to study, while not so much is known about the intermediate moduli spaces and the first one (which has strong relations with the Brill-Noether locus $B(n,d,k)$). In particular, an interesting open problem is that of computing the Hodge-Deligne polynomials of such moduli spaces. I will present some explicit results in the cases when (n=2,k=1) and (n=3,k=1), together with some general techniques that in principle could be used to tackle also more complicated cases. This is still work in progress for my Ph.D. thesis under the supervision of professor Peter Newstead.