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 Actions of Finite Groups on Varieties. II.
Free Actions of Finite Groups on Varieties. II. (Erratum).
Free pencils on divisors.
Free Resolutions of The Defining Ideal of Certain Rational Surfaces.
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 et cohomologie locale
Frobenius indices of certain curves over finite fields.
Frobenius nonclassicality with respect to linear systems of curves of arbitrary degree
For each integer s ≥ 1, we present a family of curves that are -Frobenius nonclassical with respect to the linear system of plane curves of degree s. In the case s=2, we give necessary and sufficient conditions for such curves to be -Frobenius nonclassical with respect to the linear system of conics. In the -Frobenius nonclassical cases, we determine the exact number of -rational points. In the remaining cases, an upper bound for the number of -rational points will follow from Stöhr-Voloch...
Frobenius pull-back of vector bundles of rank 2 over non-uniruled varieties.
Frobenius' theorem for differential forms on analytic spaces
From holonomy of the Ising model form factors to -fold integrals and the theory of elliptic curves.
From the elliptic regulator to exotic relations.
From the Taniyama-Shimura conjecture to Fermat's last theorem
Fuchsian groups and uniformization of Hurwitz spaces.
Fulton-Hansen and Barth-Lefschetz theorems for subvarieties of abelian varieties.
Function fields of certain arithmetic curves and application
Function Fields of Quadratic Forms.