Fourier-Mukai transform and index theory.
Fourier-Mukai transforms and stable bundles on elliptic curves.
Fragmented deformations of primitive multiple curves
A primitive multiple curve is a Cohen-Macaulay irreducible projective curve Y that can be locally embedded in a smooth surface, and such that Y red is smooth. We study the deformations of Y to curves with smooth irreducible components, when the number of components is maximal (it is then the multiplicity n of Y). We are particularly interested in deformations to n disjoint smooth irreducible components, which are called fragmented deformations. We describe them completely. We give also a characterization...
Free pencils on divisors.
Freeness of hyperplane arrangements and related topics
These are the expanded notes of the lecture by the author in “Arrangements in Pyrénées”, June 2012. We are discussing relations of freeness and splitting problems of vector bundles, several techniques proving freeness of hyperplane arrangements, K. Saito’s theory of primitive derivations for Coxeter arrangements, their application to combinatorial problems and related conjectures.
Frobenius pull-back of vector bundles of rank 2 over non-uniruled varieties.
Frobenius' theorem for differential forms on analytic spaces
Fundamental group of a class of rational cuspidal curves.
Fundamental group of locally symmetric varieties.
Fundamental groups and Diophantine geometry
This is a brief exposition on the uses of non-commutative fundamental groups in the study of Diophantine problems.