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- Boris Pasquier
- 2008

We describe smooth projective horospherical varieties with Picard number 1. Moreover we prove that the automorphism group of any such variety acts with at most two orbits and we give a geometric characterisation of non-homogeneous ones.

For a few pairs (G ⊂ ˆ G) of reductive groups, we study the decomposition of irreduciblê G-modules into G-modules. In particular, we observe the saturation property for all of these pairs.

- Boris Pasquier
- 2012

We describe the Minimal Model Program in the family of Q-Gorenstein projective horo-spherical varieties, by studying a family of polytopes defined from the moment polytope of a Cartier divisor of the variety we begin with. In particular, we generalize the results on MMP in toric varieties due to M. Reid, and we complete the results on MMP in spherical… (More)

- Boris Pasquier
- 2013

We classify all smooth projective horospherical varieties with Picard number 1. We prove that the automorphism group of any such variety X acts with at most two orbits and that this group still acts with only two orbits on X blown up at the closed orbit. We characterize all smooth projective two-orbit varieties with Picard number 1 that satisfy this latter… (More)

- Boris Pasquier
- 2008

We use the Grossberg-Karshon's degeneration of Bott-Samelson varieties to toric varieties and the description of cohomolgy of line bundles on toric varieties to deduce vanishing results for the cohomology of lines bundles on Bott-Samelson varieties.

- Boris Pasquier
- 2008

We classify all smooth projective horospherical varieties with Picard number 1. We prove that the automorphism group of any such variety X acts with at most two orbits and that this group still acts with only two orbits on X blown up at the closed orbit. We characterize all smooth projective two-orbits varieties with Picard number 1 that satisfy this latter… (More)

Let X be a minuscule homogeneous space, an odd-dimensional quadric, or an adjoint homogenous space of type different from A and G 2. Le C be an elliptic curve. In this paper, we prove that for d large enough, the scheme of degree d morphisms from C to X is irreducible, giving an explicit lower bound for d which is optimal in many cases.

- Boris Pasquier
- 2010

We prove a conjecture of L. Bonavero, C. Casagrande, O. Debarre and S. Druel, on the pseudo-index of smooth Fano varieties, in the special case of horospherical varieties. Let X be a normal, complex, projective algebraic variety of dimension d. Assume that X is Fano, namely the anticanonical divisor −K X is Cartier (in other words, X is Gorenstein) and… (More)

For a G-variety X with an open orbit, we define its boundary ∂X as the complement of the open orbit. The action sheaf S X is the subsheaf of the tangent sheaf made of vector fields tangent to ∂X. We prove, for a large family of smooth spherical varieties, the vanishing of the cohomology groups H i (X, S X) for i > 0, extending results of F. Bien and M.… (More)

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