Positivity properties of relative complete intersections
We give conditions for $f$-positivity of relative complete intersections in projective bundles. We also derive an instability result for the fibres.
math.AG↗
arXiv subjects
L. Stoppino
Publications and source records attributed to L. Stoppino.
Stability and singularities of relative hypersurfaces
We study relative hypersurfaces over curves, and prove an instability condition for the fibres. This gives an upper bound on the log canonical threshold of the relative hypersurface. We compare these results with the information that can be derived from Nakayama's Zariski decomposition of effective divisors on relative projective bundles.
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A sharp bound for the slope of double cover fibrations
Let f: X->B be a fibred surface of genus g whose general fibre is a double cover of a smooth curve of genus gamma. We show that, for g > 4gamma+1, the number 4(g-1)/(g-gamma) is a sharp lower bound for the slope of f, proving a conjecture of Barja. Moreover, we give a characterisation of the fibred surfaces that reach the bound. In the case g = 4gamma+1 we obtain the same sharp bound under the assumption that the involutions on the general fibres glue to a global involution on X.
math.AG↗
Linear stability of projected canonical curves with applications to the slope of fibred surfaces
Let f :S\to B be a non locally trivial fibred surface. We prove a lower bound for the slope of f depending increasingly from the relative irregularity of f and the Clifford index of the general fibres.
math.AG↗