We study the quantum cohomology of (co)minuscule homogeneous varieties under a unified perspective. We show that three points Gromov-Witten invariants can always be interpreted as classicalâ€¦ (More)

We study the quantum cohomology of quasi-minuscule and quasi-cominuscule homogeneous spaces. The product of any two Schubert cells does not involve powers of the quantum parameter higher than 2. Withâ€¦ (More)

We prove that the quantum cohomology ring of any minuscule or cominuscule homogeneous space, once localized at the quantum parameter, has a non trivial involution mapping Schubert classes toâ€¦ (More)

Let X be a rational homogeneous space and let QH(X)Ã— loc be the group of invertible elements in the small quantum cohomology ring of X localised in the quantum parameters. We generalise results ofâ€¦ (More)

We prove that the quantum cohomology ring of any minuscule or cominuscule homogeneous space, once localized at the quantum parameter, has a non trivial involution mapping Schubert classes toâ€¦ (More)

This paper gathers results obtained with a software written in Java, accessible on the web-page For exceptional minuscule, quasi-minuscule, cominus-cule or adjoint homogeneous spaces, the Schubertâ€¦ (More)

After giving an explicit description of all the non vanishing Dolbeault cohomology groups of ample line bundles on grassmannians, I give two series of vanishing theorems for ample vector bundles on aâ€¦ (More)

For a split semisimple Chevalley group scheme G with Lie algebra g over an arbitrary base scheme S, we consider the quotient of g by the adjoint action of G. We study in detail the structure of gâ€¦ (More)