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Fragmented deformations of primitive multiple curves

100%

Drézet J.-M.

Open Mathematics

2013

tom 11

nr 12

2106-2137

A primitive multiple curve is a Cohen-Macaulay irreducible projective curve Y that can be locally embedded in a smooth surface, and such that Y red is smooth. We study the deformations of Y to curves with smooth irreducible components, when the number of components is maximal (it is then the multiplicity n of Y). We are particularly interested in deformations to n disjoint smooth irreducible components, which are called fragmented deformations. We describe them completely. We give also a characterization of primitive multiple curves having a fragmented deformation.

Jacobi-Bernoulli cohomology and deformations of schemes and maps

70%

Ran Z.

Open Mathematics

2012

tom 10

nr 4

1541-1591

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.

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2 Open Mathematics

1 Drézet J.-M.

1 Ran Z.

1 2013

1 2012

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Fragmented deformations of primitive multiple curves

Jacobi-Bernoulli cohomology and deformations of schemes and maps