Mathematics – Algebraic Geometry
Scientific paper
2000-03-29
Mathematics
Algebraic Geometry
18 pages in french
Scientific paper
In this article we prove the irreducibility of the Hilbert scheme of rationnal curves on homogeneous varieties with fixed class in the Chow ring. This result has also been proved by J. F. Thomsen [T] and B. Kim and R. Pandharipande [KP]. Our method is totaly different (we don't use the compactification of stable maps) and enables us to prove the existence of rational smooth curves on homogeneous varities with fixed class in the Chow ring. This was not the case of Thomsen's and Kim and Pandharipande's proofs. We use a decomposition of G/P in orbits (called the P'-orbits, see definition) which are bigger than the Schubert cells. We then prove that these P'-orbits are "towers" of affine bundles (see definition) over "smaller" homogeneous varities. This description gives the results. Our decomposition in P'-orbits enables us to give a "better" desingularisation of Schubert varities than Demazure's one.
No associations
LandOfFree
Courbes rationnelles sur les variétés homogènes et une désingularisation plus fine des variétés de Schubert does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Courbes rationnelles sur les variétés homogènes et une désingularisation plus fine des variétés de Schubert, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Courbes rationnelles sur les variétés homogènes et une désingularisation plus fine des variétés de Schubert will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-682974