Caro Bruno,

ti segnalo che questo si sovrappone con il seminario del ciclo di Luca Migliorini sulla Teoria di Hodge.

Ciao, Angelo

On 10 Nov 2014, at 19:54, Bruno Martelli martelli@dm.unipi.it wrote:

buondì,

vi segnalo il seminario di geometria di domani. a presto, Bruno

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Tuesday, November 11, 2014

Aula seminari, ore 14:00

Title: On the Dolbeault cohomological dimension of the moduli space of Riemann surfaces

Speaker: Gabriele Mondello

Abstract:

The moduli space M_g of Riemann surfaces of genus g is (up to a finite étale cover) a complex manifold and so it makes sense to speak of its Dolbeault cohomological dimension (i.e. the highest k such that H^{0,k}(M_g,E) does not vanish for some holomorphic vector bundle E on M_g). The conjecturally optimal bound is g-2, which is verified for g=2,3,4,5. In this talk, I will show that such dimension is at most 2g-2. The key point is to show that the Dolbeault cohomological dimension of each stratum of the Hodge bundle is at most g (still non-optimal bound). In order to do that, I produce an exhaustion function, whose complex Hessian has controlled index: in the construction of such a function basic geometric properties of translation surfaces come into play. _______________________________________________ Geometria_Pisa mailing list Geometria_Pisa@mail.dm.unipi.it https://mail.dm.unipi.it/listinfo/geometria_pisa