Selected papers
(here a
much longer list in reverse order)
A. H. - C. Simpson: Descente pour les n-champs.
on alg-geom e-prints: 9807049.
Etat 0 for a theory of higher stacks. The final version is delayed.
J. Alexander-A.H.: An asymptotic vanishing theorem for
generic unions of multiple points. Invent. Math. 140 (2000) 2, 303-325.
We prove by
a new differential Horace method that generic unions of sufficiently many
fat points of bounded multiplicity in any projective variety have the maximal
rank property.
Ph. Ellia -A. H.- L. Manivel:
Le problème de Brill-Noether pour les fibrés
de Steiner et application aux courbes gauches. Annales ENS Paris 32 (1999)
835-857.
We construct generic space curves with nice resolutions, comme au bon vieux
temps.
A.H.-S. Ramanan:
New evidence for Green's conjecture on syzygies
of canonical curves. Ann. ENS Paris 31, 145-152 (1998).
We make some
computations in the
Picard group of the moduli stack showing, for odd genus, that if the generic
curve has the expected canonical resolution then so does any curve outside
the evident (k-gonal) divisor.
L. Göttsche-A. H.: Weak Brill-Noether theorem for
vector bundles on the projective plane: in
Algebraic Geometry: Papers Presented for the
Europroj Conferences in Catania and Barcelona, Marcel Dekker(1998) 63-74.
Dans les bons cas, les fibrés à cohomologie non-naturelle
n'apparaissent pas en codimension un dans les modules de fibrés stables
sur le plan. Ce résultat avait été commandé par Le
Potier (voir ce qu'il en fait dans le même volume).
G. Ellingsrud-A.H.: Sur le fibré normal des courbes
gauches. C.R.A.S. 299 (1984) 245-248.
We apply degeneration techniques in order to prove that the normal bundle of
most good (eg nonspecial) generic space curves is stable with natural cohomology.
R. Hartshorne-A. H.: Cohomology of a general instanton bundle
Ann. Sc. ENS
Paris,15, 365-390 (1982).
The scope of the méthode d'Horace is extended
to the cohomology of vector bundles and a conjecture of Hartshorne is proved.
A. H.:
On the convergence of formal equivalence between embeddings. (English)
[J] Ann. Math., II. Ser. 113, 501-514 (1981).
A new geometric method is introduced
for proving convergence of formal equivalences, and the so-called formal
principle is extended beyond earlier results of Griffiths and Hartshorne
(among others).
A. H.:
Sur la postulation generique des courbes rationnelles. Acta Math. 146, 209-230
(1981).
In this paper is introduced the so-called "méthode d'Horace" for postulation
problems, which will be reused and enlarged many times.
Here a conjecture of Hartshorne is settled.
A.H.- A. Piriou, A.
Propriétés de transmission pour les distributions inté
grales de Fourier.
Commun. Partial Differ. Equations 4, 113-217 (1979).
A whole theory is
developed
for these symmetries of distributions; this theory incorporates original
considerations concerning indices (or signatures) associated
(à la Maslov)
to configurations of Lagrangian subspaces of a symplectic vector space.
A. H.:
Le problème de Levi pour les espaces homogènes.
Bull. Soc. math. France 103, 191-201 (1975).
A truly geometric (and not constructive)
proof of the existence of strictly plurisubharmonic
functions on (most) locally pseudoconvex open subsets of homogeneous
manifolds.
A. H.:
Remarques sur les ouverts d'holomorphie d'un produit dénombrable de droites.
Ann. Inst. Fourier 19, No.1, 219-229 (1969).
Could be interesting from an
ethnological point of view, or if you want to get a feeling about my
mathematical roots. By the way, some results at the very end of the paper are
litigious as was pointed out (in 1999 !) by Murielle Mauer (Liege).
Dernière mise à jour: 4 mai 00.