|Born||25 September 1957|
|Died||17 March 2022 (aged 64)|
|Alma mater||École Normale Supérieure|
Paris Diderot University
Pierre and Marie Curie University
|Institutions||Université Grenoble Alpes|
|Thesis||Sur différents aspects de la positivité en analyse complexe (1982)|
|Doctoral advisor||Henri Skoda|
Jean-Pierre Demailly (25 September 1957 – 17 March 2022) was a French mathematician who worked in complex geometry. He was a professor at Université Grenoble Alpes and a permanent member of the French Academy of Sciences.
Early life and education
Demailly was born on 25 September 1957 in Péronne, France. He attended the Lycée de Péronne from 1966 to 1973 and the Lycée Faidherbe from 1973 to 1975. He entered the École Normale Supérieure in 1975, where he received his agrégation in 1977 and graduated in 1979. During this time, he received an undergraduate licence degree from Paris Diderot University in 1976 and a diplôme d'études approfondies under Henri Skoda at the Pierre and Marie Curie University in 1979. He received his Doctorat d'État in 1982 under the direction of Skoda at the Pierre and Marie Curie University, with thesis "Sur différents aspects de la positivité en analyse complexe".
Demailly became a professor at Université Grenoble Alpes in 1983. He served as the editor-in-chief of the Annales de l'Institut Fourier from 1998 to 2006 and the editor-in-chief of Comptes Rendus Mathématique from 2010 to 2015. He was also an editor for Inventiones Mathematicae from 1997 to 2002.
He was the director of the Institut Fourier from 2003 to 2006. From June 2003 onwards, he led the Groupe de réflexion interdisciplinaire sur les programmes (GRIP), which ran experimental classes in primary schools.
Demailly's mathematical works primarily concerned complex analytic geometry, using techniques from complex geometry with applications to algebraic geometry and number theory. He also wrote and co-authored several Unix and Linux libraries starting in the 1990s, including xpaint, sunclock, and dmg2img.
One main topic of Demailly's research is Pierre Lelong's generalization of the notion of a Kähler form to allow forms with singularities, known as currents. In particular, for a compact complex manifold , an element of the Dolbeault cohomology group is called pseudo-effective if it is represented by a closed positive (1,1)-current (where "positive" means "nonnegative" in this phrase), or big if it is represented by a strictly positive (1,1)-current; these definitions generalize the corresponding notions for holomorphic line bundles on projective varieties. Demailly's regularization theorem says, in particular, that any big class can be represented by a Kähler current with analytic singularities.
Such analytic results have had many applications to algebraic geometry. In particular, Boucksom, Demailly, Păun, and Peternell showed that a smooth complex projective variety is uniruled if and only if its canonical bundle is not pseudo-effective.
For a singular metric on a line bundle, Nadel, Demailly, and Yum-Tong Siu developed the concept of the multiplier ideal, which describes where the metric is most singular. There is an analog of the Kodaira vanishing theorem for such a metric, on compact or noncompact complex manifolds. This led to the first effective criteria for a line bundle on a complex projective variety of any dimension to be very ample, that is, to have enough global sections to give an embedding of into projective space. For example, Demailly showed in 1993 that is very ample for any ample line bundle L, where addition denotes the tensor product of line bundles. The method has inspired later improvements in the direction of the Fujita conjecture.
Demailly used the technique of jet differentials introduced by Green and Phillip Griffiths to prove Kobayashi hyperbolicity for various projective varieties. For example, Demailly and El Goul showed that a very general complex surface of degree at least 21 in projective space is hyperbolic; equivalently, every holomorphic map is constant. For any variety of general type, Demailly showed that every holomorphic map satisfies some (in fact, many) algebraic differential equations.
Awards and honors
Demailly received the CNRS Bronze Medal in 1981, the Prix Mergier-Bourdeix from the French Academy of Sciences in 1994, the Humboldt Prize in 1996, the Simion Stoilow Prize from the Romanian Academy of Sciences in 2006, the Stefan Bergman Prize from the American Mathematical Society in 2015, and the Heinz Hopf Prize from ETH in 2021.
Demailly was elected a correspondent of the French Academy of Sciences in 1994 and then became a permanent member in 2007. He was an invited speaker at the International Congress of Mathematicians in 1994 and a plenary speaker in 2006.
Demailly died on 17 March 2022.
- "Curriculum Vitae". Jean-Pierre Demailly (in French). Retrieved 19 March 2022.
- "Jean-Pierre Demailly" (PDF). French Academy of Sciences (in French). Retrieved 19 March 2022.
- Jean-Pierre Demailly at the Mathematics Genealogy Project
- "Mathematics People". Notices of the American Mathematical Society. 63 (4): 445–447. 2016.
- Demailly (1992); Demailly (2012), Corollary 14.13.
- Boucksom et al. (2013); Lazarsfeld (2004), Corollary 11.4.20.
- Lazarsfeld (2004), Ch. 9; Demailly (2012), Theorem 5.11.
- Demailly (2012), Theorem 7.4.
- Demailly & El Goul (2000).
- Demailly (2011); Demailly (2012), Theorem 9.5.
- "Prix Mergier Bourdeix" (PDF). French Academy of Sciences. Retrieved 19 March 2022.
- "Heinz Hopf Prize and Lectures". ETH Zurich. Retrieved 19 March 2022.
- "Jean-Pierre Demailly | Liste des membres de l'Académie des sciences / D | Listes par ordre alphabétique | Listes des membres | Membres | Nous connaître". academie-sciences.fr. Retrieved 2 March 2017.
- "ICM Plenary and Invited Speakers". International Mathematical Union. Retrieved 19 March 2021.
- "Décès de Jean-Pierre Demailly". Société mathématique de France (in French). 18 March 2022. Retrieved 19 March 2022.
- Boucksom, Sébastien; Demailly, Jean-Pierre; Păun, Mihai; Peternell, Thomas (2013), "The pseudo-effective cone of a compact Kähler manifold and varieties of negative Kodaira dimension", Journal of Algebraic Geometry, 22 (2): 201–248, arXiv:math/0405285, doi:10.1090/S1056-3911-2012-00574-8, MR 3019449, S2CID 15197055
- Demailly, Jean-Pierre (2012), Analytic Methods in Algebraic Geometry (PDF), International Press, ISBN 978-1-57146-234-3, MR 2978333
- Demailly, Jean-Pierre (2011), "Holomorphic Morse inequalities and the Green–Griffiths–Lang conjecture", Pure and Applied Mathematics Quarterly, 7 (4): 1165–1207, arXiv:1011.3636, doi:10.4310/PAMQ.2011.v7.n4.a6, MR 2918158, S2CID 16065414
- Lazarsfeld, Robert (2004), Positivity in Algebraic Geometry (2 vols.), Springer Nature, ISBN 978-3-540-22533-1, MR 2095471
- Demailly, Jean-Pierre; Kollár, János (2001). "Semi-continuity of complex singularity exponents and Kähler–Einstein metrics on Fano orbifolds". Annales Scientifiques de l'École Normale Supérieure. 34 (4): 525–556. doi:10.1016/S0012-9593(01)01069-2. MR 1852009. S2CID 14301604.
- Demailly, Jean-Pierre; El Goul, Jawher (2000), "Hyperbolicity of generic surfaces of high degree in projective 3-space", American Journal of Mathematics, 122 (3): 515–546, arXiv:math/9804129, doi:10.1353/ajm.2000.0019, MR 1759887, S2CID 14166985
- Demailly, Jean-Pierre (1992), "Regularization of closed positive currents and intersection theory" (PDF), Journal of Algebraic Geometry, 1: 361–409, MR 1158622
- Demailly, Jean-Pierre (1982). "Estimations pour l'opérateur d'un fibré vectoriel holomorphe semi-positif au-dessus d'une variété kählérienne complète". Annales Scientifiques de l'École Normale Supérieure. 15 (3): 457–511. doi:10.24033/asens.1434. MR 0690650.