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Semi-continuity of complex singularity exponents and K\
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The Nash problem on arc families of singularities
Nash [21] proved that every irreducible component of the space of arcs through a singularity corresponds to an exceptional divisor that appears on every resolution. He asked if the converse also…
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Szemer\'edi--Trotter-type theorems in dimension 3
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Kähler-Einstein metrics on log Del Pezzo surfaces in weighted projective 3-spaces
Nous determinons toutes les surfaces de del Pezzo logarithmiques quasi-lisses dans les espaces projectifs a poids de dimension 3, qui sont plongees par leur morphisme anticanonique. Beaucoup de ces…
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Einstein metrics on spheres
We prove the existence of an abundance of new Einstein metrics on odd dimensional spheres including exotic spheres, many of them depending on continuous parameters. The number of families as well as…
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The dual complex of singularities
The dual complex of a singularity is defined, up-to homotopy, using resolutions of singularities. In many cases, for instance for isolated singularities, we identify and study a "minimal"…
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Remarks on degenerations of hyper-K\"ahler manifolds
Using the Minimal Model Program, any degeneration of K-trivial varieties can be arranged to be in a Kulikov type form, i.e. with trivial relative canonical divisor and mild singularities. In the…
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Holonomy Groups of Stable Vector Bundles
We define the notion of holonomy group for a stable vector bundle F on a variety in terms of the Narasimhan‐Seshadri unitary representation of its restriction to curves. Next we relate the holonomy…
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Rational Curves on Varieties
The aim of these notes is to give an introduction to the ideas and techniques of handling rational curves on varieties. The main emphasis is on varieties with many rational curves, which are the…
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Which powers of holomorphic functions are integrable
We show that every limit of log canonical thresholds of n-variable functions is also a log canonical threshold of an (n-1)-variable function.
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