A few remarks about the variety of irreducible plane curves of given degree and genus
A few remarks on blowing-up and connectedness.
A filtered Bertini-type theorem.
A Finiteness Property of Varieties of General Type.
A finiteness result for the compactly supported cohomology of rigid analytic varieties, II
Let be a separated morphism of adic spaces of finite type over a non-archimedean field with affinoid and of dimension , let be a locally closed constructible subset of and let be the morphism of pseudo-adic spaces induced by . Let be a noetherian torsion ring with torsion prime to the characteristic of the residue field of the valuation ring of and let be a constant -module of finite type on . There is a natural class of -modules on generated by the constructible -modules...
A finiteness theorem for the symmetric square of an elliptic curve.
A finiteness theorem for unpolarized Abelian varieties over number fields with prescribed places of bad reduction.
A first-order version of Pfaffian closure
The purpose of this paper is to extend a theorem of Speissegger [J. Reine Angew. Math. 508 (1999)], which states that the Pfaffian closure of an o-minimal expansion of the real field is o-minimal. Specifically, we display a collection of properties possessed by the real numbers that suffices for a version of the proof of this theorem to go through. The degree of flexibility revealed in this study permits the use of certain model-theoretic arguments for the first time, e.g. the compactness theorem....
A Fixed Point Formula for Action of Tori on Algebraic Varieties.
A fixed point formula for varieties over finite fields.
A fixed point formula of Lefschetz type in Arakelov geometry II: A residue formula
This is the second of a series of papers dealing with an analog in Arakelov geometry of the holomorphic Lefschetz fixed point formula. We use the main result of the first paper to prove a residue formula "à la Bott" for arithmetic characteristic classes living on arithmetic varieties acted upon by a diagonalisable torus; recent results of Bismut- Goette on the equivariant (Ray-Singer) analytic torsion play a key role in the proof.
A footnote to a paper by Noma
Let be a globally generated ample vector bundle of rank on a complex projective smooth surface . By extending a recent result by A. Noma, we classify pairs as above satisfying .
A footnote to the Poincaré complete reducibility theorem.
Poincaré's work on the reduction of Abelian integrals contains implicitly an algorithm for the expression of a theta function as a sum of products of theta functions of fewer variables in the presence of reduction. The aim of this paper is to give explicit formulations and reasonably complete proofs of Poincaré's results.
A formula for the Cartier operator on plane algebraic curves.
A Formula for the Euler characteristic of a real algebraic manifold.
A Foruier-Mukai transform for stable bundles on K3 surfaces.
A functional equation originating from elliptic curves.
A fundamental domain for the Fermat curves and their quotients.
A gallery of iterated correspondences.
A GAP package for braid orbit computation and applications.