Jean-Pierre Demailly

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. 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.

Career Demailly became a professor at Université Grenoble Alpes in 1983.

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.

Multiplier ideals 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.

Kobayashi hyperbolicity 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 Humboldt Prize in 1996, 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.

In 2024, the Jean-Pierre Demailly prize for open science in mathematics is created in his honor. It is awarded every two years.

In 2025, the Société mathématique de France published a special issue of its gazette in his memory.

Death Demailly died on 17 March 2022.