The Atiyah extension of a Lie algebra deformation.
Cycles on Fermat hypersurfaces
The structure of Gauss-like maps
Surfaces of order 1 in Grassmannians.
A Characterization of Five-Dimensional Jacobian Varieties.
On Subvarieties of Abelian Varieties.
The (dimension + 2)-secant Lemma.
Jacobi-Bernoulli cohomology and deformations of schemes and maps
We introduce a notion of Jacobi-Bernoulli cohomology associated to a semi-simplicial Lie algebra (SELA). For an algebraic scheme X over ℂ, we construct a tangent SELA J X and show that the Jacobi-Bernoulli cohomology of J X is related to infinitesimal deformations of X.
Hodge theory and deformations of maps
Enumerative geometry of divisorial families of rational curves
We compute the number of irreducible rational curves of given degree with 1 tacnode in or 1 node in meeting an appropriate generic collection of points and lines. As a byproduct, we also compute the number of rational plane curves of degree passing through given points and tangent to a given line. The method is ‘classical’, free of Quantum Cohomology.
Semiregularity, obstructions and deformations of Hodge classes
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