Niveau: Supérieur, Doctorat, Bac+8
IMRN International Mathematics Research Notices 1997, No. 19 On the Moduli of SL(2)-bundles with Connections on P1 n fx1; : : : ; x4g D. Arinkin and S. Lysenko Introduction The moduli spaces of bundles with connections on algebraic curves have been studied from various points of view (see [6]; [10]). Our interest in this subject was motivated by its relation with the Painleve equations; and also by the important role of bundles with connections in the geometric Langlands program [4] (for more details see the remarks at the end of the introduction). In this work; we consider SL(2)-bundles on P1 with connections. These connec- tions are supposed to have poles of order 1 at fixed n points; and the eigenvalues ‚i of the residues are fixed. We call these bundles (‚1; : : : ; ‚n)-bundles. Our aim is to find all invertible sheaves on the moduli space of (‚1; : : : ; ‚n)-bundles and to compute the cohomology of these sheaves for n D 4. In this work; the ground field is C; that is; ‘space' means ‘C-space'; P1 means P1C; and so on. Let us formulate the main results of this work.
- then
- moduli space
- gerbe over
- let l1 ‰
- id1 resxi
- p1k ‰
- equation pvi
- picard group ofm