Annales de l’institut Fourier (AIF)

Benea, Cristina

Bernicot, Frédéric

Conservation de certaines propriétés à travers un contrôle épars d’un opérateur et applications au projecteur de Leray–Hopf

Fan, Aihua

Schmeling, Jörg

Everywhere divergence of one-sided ergodic Hilbert transform

Gruber, Dominik

Sisto, Alessandro

Infinitely presented graphical small cancellation groups are acylindrically hyperbolic

Zimmer, Andrew M.

Proper quasi-homogeneous domains in flag manifolds and geometric structures

Barbot, Thierry

Lee, Gye-Seon

Valério, Viviane Pardini

Pappus Theorem, Schwartz Representations  and Anosov Representations

Peternell, Thomas

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L’INSTITUT FOURIER
Thomas PETERNELL
Jean-Pierre: some personal reminiscences
Tome 68, no 7 (2018), p. 2779-2781.
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68, 7 (2018) 2779-2781
JEAN-PIERRE: SOME PERSONAL REMINISCENCES
by Thomas PETERNELL
My first contact with Jean-Pierre was on the occasion of a conference
on complex analysis in Trento, held in the beautiful Villa Madruzzo in
june 1983 - Jean-Pierre gave a lecture on positive closed currents at that
conference. Apart from mathematics, I still remember at least one joint
soccer match during one of these meetings which took place every year
in early summer. We were in the same team, a hint for the future. At
that time (1983) he already held a professor position in Grenoble. One of
his first visits to Bayreuth was in 1990 to speak at a conference “Complex
Algebraic Varieties” which I organized with Klaus Hulek, Michael Schneider
and Frank-Olaf Schreyer. This was - shortly after the dramatic political
changes in 1989 - one of the first international meetings with participants
both from the West and the East. Jean-Pierre lectured on “A numerical
criterion for very ample line bundles”; one of his numerous breakthroughs
in Complex Analysis and Algebraic Geometry and the starting point for all
subsequant developments around the Fujita Conjecture. His contribution
to the proceedings of this conference, appearing as Springer Lecture Notes
1507, is the extremely influential article “Singular metrics on positive line
bundles”. Not only did he introduce the important notion of a singular
hermitian metric on a holomorphic line bundle which allows in particular to
characterize pseudoeffective line bundles by the positivity of the curvature
current of a singular metric. But he also invented the notion of Seshadri
constants for nef line bundles, a measure for positivity, which have been
studied in numerous research articles since then.
Around 1990 we started, together with Michael Schneider, joint research
projects. The first paper studied compact Kähler manifolds X whose tan-
gent bundle are nef, a geometric version of having a metric with semiposi-
tive holomorphic bisectional curvature. A priori, the nefness assumption is
2780 Thomas PETERNELL
weaker than the metric assumption. We proved structure theorems which
gave a rather precise picture of those manifolds up to a central conjecture
which states a Fano manifold with nef tangent bundle must be rational-
homogeneous. Despite many efforts and results in special cases, this conjec-
ture is still very much open. Our collaboration was sponsored at that time
by a French-German program, called PROCOPE, financing mutual visits.
In the following decades, we studied compact Kähler manifolds with nef an-
ticanonical bundles followed, pseudoeffective line bundles, in particular in
connection with the nonvanishing and the abundance conjecture, further-
more line bundles with some partial positivity and as well the geometry of
special varieties.
Actually, despite a unified Europe, a travel from Grenoble to Bayreuth or
the other way around was, and is not that easy, taking some time. Usually
Jean-Pierre took a night train from Paris in a couchette, a compartment
with six people. For our part, we enjoyed the hospitality of the Hotel Gloria
and the Hotel des Alpes during visits to Grenoble. Of course, Grenoble has
the advantage of being a real city, located in a beautiful landscape and,
last but not least, not too far from Burgundy.
Needless to say, we met at many conferences. A very sad occasion was the
Bayreuth memorial conference 1998 for our friend Michael Schneider. Here
Jean-Pierre lectured on “Almost complex projective embeddings of compact
real symplectic manifolds” a very broad and general subject outside Kähler
geometry.
Jean-Pierre has special connections to Göttingen (my Alma Mater),
equivalently to Hans Grauert. Shortly after the solution by Y.T.Siu, he
showed that the Grauert-Riemenschneider Conjecture is a consequence of
his famous holomorphic Morse inequalities which he developped in the late
80’s. Moreover he received the Dannie Heinemann Prize from the Acad-
emy of Science in Göttingen in 1991. Needless to say, he was one of the
main speakers in the conference of honour of Grauert’s 70th birthday, held
in Göttingen in 2000, with a lecture on “Subadditivity of multiplier ideal
sheaves and asymptotic Zariski decomposition”. He also contributed an
extremely elegant article “On the Frobenius integrability of certain holo-
morphic p-forms”, which had its origin - and was wrapped up - during the
conference. Namely, jointly with Stefan Kebekus, Andrew Sommese and
Jaroslaw Wiśniewski, I was studying projective contact manifolds X with
second Betti number at least two. In order to prove our structure theorem
for these manifolds we needed the fact that the canonical bundle of X is
not nef. So, we asked Jean-Pierre and he solved the problem (in a much
ANNALES DE L’INSTITUT FOURIER
JEAN-PIERRE: SOME PERSONAL REMINISCENCES 2781
more general setting and establishing an integrabiltiy theorem) during the
conference - without even missing talks, I guess.
The Complex Analysis meetings in Oberwolfach - the institute located
more or less half way between Grenoble and Bayreuth - in late August every
other year are a great tradition, going back to the early 50’s. For a long
period they were organized by Grauert-Remmert-Stein and later Grauert-
Remmert-Barth. It was absolutely natural that Jean-Pierre should become
an organizer, and I had the pleasure to work with him and Klaus Hulek in
this function from 1996 to 2012.
The mathematical influence of Jean-Pierre cannot be overestimated. He
introduced important techniques such as his regularization of closed pos-
itive currents, his holomorphic Morse inequalities (as already mentioned),
enforced the study of the multiplier ideal and the use of Monge-Ampère
equations. His new methods in the study of hyperbolicity are indispensable.
The scientific and the personal appreciation of Jean-Pierre was mani-
fested in a conference in Grenoble in June 2017 in his honour with a large
number of outstanding mathematicians participating and an illustrious pro-
gram - and by this volume.
Of course, these are just a few personal remarks and views. It would take
many pages to give a detailed overview over the extraordinary mathemat-
ical work of Jean-Pierre (and it would be only temporarily!), not to speak
of his mathematical school with many extremely successful students and
his further numerous activities: organizing science, publication of science
(the Episcience project), school education in France, and nuclear energy
problems. Better not even to try!
Thomas PETERNELL
Mathematisches Institut
Universität Bayreuth
95440 Bayreuth (Germany)
thomas.peternell@uni-bayreuth.de
TOME 68 (2018), FASCICULE 7


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