Towards slope inequalities of fibred varieties over surfaces
Working on previous work of T. Zhang, we construct a new invariant associated to a coherent sheaf on a surface, the positive second Chern character. We will see that this positive invariant is a natural object to study slopes of fibrations over surfaces and I will present a Severi-type slope inequality for those of maximal Albanese dimension.
This is a joint work in progress with Martí Lahoz and Andrés Rojas.