I was born in 1962 in a small town in the Northern suburbs of Paris. My parents married in 1945 and had nine children before me (they ended-up with twelve children), so I grew up with many sisters and brothers, most of them older than me, in a curious atmosphere influenced by the 60’s spirit but also very much turned towards intellectual life. My father was an engineer who liked science and taught me a lot of classical geometry (circle and triangle) and my mother, who had stopped studying during the Second World War, was very fond of art. She was extremely enthusiastic about Impressionist painting and the subsequent development of Modern Art. She began studying history of art at Ecole du Louvres when she was in her 50’s. I left the family home when I was seventeen having gained a Fellowship from the government, and studied first for two years in Classes préparatoires at Lycée Louis-le-Grand. I then entered Ecole normale supérieure of Sèvres: at that time the female branch of ENS was still separated from Ulm, which accepted only male students. There and at Jussieu I studied most sorts of mathematics until I started my PhD thesis at Orsay under the direction of Arnaud Beauville. My thesis, proving the Torelli theorem for cubic fourfolds, already involved the theory of Hodge structures developed by Griffiths, which is still an ingredient of a large part of my research, being a rich tool to study many different sorts of questions concerning algebraic varieties and their moduli.
I defended my PhD thesis in 1986, the same year I got a permanent research position at CNRS, which I kept until 2016. I am now Professor at Collège de France, which is a different institution. In 1984, I married Mathematician Jean- Michel Coron and we have five children, born between 1987 and 1997. In 1987, I met Kollár who at that time was Professor at the University of Utah in Salt Lake City where I was supposed to stay as a postdoc with Herb Clemens but having left my baby in Paris, I found the separation too hard and after one month finally decided to return. Starting from that period, for many years I spent most of my time at home, except of course for attending seminars, and found it very convenient doing research there. Now that our children are grown up, I travel much more, but sometimes I regret the period where my life was mostly centred at home and divided between doing research and raising my children. Of course, I owe much to the French system of childcare and also to my husband who always shared all the family duties with me. In the 2000’s, at the week-ends we used to work in a quiet place close to our house: I went there to work in the morning when I felt more fresh, and Jean-Michel worked there in the afternoon.
For a long period, between 1989 and 2012, we lived in Bourg-la-Reine in the South of Paris, in a big family house that was perfect for a large family and had a lot of character, but proved hard to sell when we decided to start a new life in Paris as our children had started to leave. We now live in the 5th arrondissement, a very quiet part of Paris where many institutes are traditionally located, like Sorbonne, Institut Henri Poincaré, Collège de France and Ecole Normale Supérieure. I like this area of Paris, sometimes called Montagne Sainte-Geneviève or Quartier latin, where I had previously lived when I was a student in Lycée Louis-le-Grand, and also later on when I attended courses at Jussieu.
The period 2002–2005 has been quite good for my research. I obtained results on syzygies of curves (the Green conjecture for generic canonical curves), a part of my research which does not involve Hodge theory, then I solved negatively the Kodaira problem, constructing compact Kähler manifolds not homeomorphic to projective ones. This work, to the contrary, was entirely based on the formal study of Hodge structures. The next work I am particularly proud of is my recent contribution to the Lüroth problem, giving a method to detect irrational varieties. This work has known many spectacular further developments. There are many other aspects of algebraic geometry I am interested in, like Chow groups and the Bloch conjectures, hyper-Kähler manifolds (construction and moduli), positivity problems for cycles, variations of Hodge structures etc. In fact, as I get older, I find there are more and more open problems I would like to attack.
What I like in algebraic geometry is a good balance between algebra and geometry and also a good balance between the theory (due to the major foundational work of the 1950–60’s) and the objects: the geometry provides a rich sample of classes of objects and discovering the adequate tools to understand these various classes and distinguish them is actually interesting and makes us fully appreciate the general theoretical machinery at our disposal (e.g. Hodge theory, or K-theory and Chow groups, and of course, more general algebraic geometry, schemes, cohomology theory, moduli, Hilbert schemes…).
26 September 2017 Hong Kong
