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.
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arXiv subjects
M. A. Barja
Publications and source records attributed to M. A. Barja.
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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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.
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On the topological index of irregular surfaces
We study the topological index of some irregular surfaces that we call generalized Lagrangian. We show that under certain hypotheses on the base locus of the Lagrangian system the topological index is non-negative. For the minimal surfaces of general type with q=4 and p_g=5 we prove the same statement without any hypotheses. Some similar results for higher dimensional varieties are given.
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