Publications

2000

• On branch points of superminimal surfaces in 4-manifolds
  
  • Ville Marina
  The Journal of Geometric Analysis, Springer, 2000, 10 (3), pp.565-573. (10.1007/BF02921950)
  DOI : 10.1007/BF02921950
• Estimated transversality in symplectic geometry and projective maps
  
  • Auroux Denis
  , 2000. The main theorem of this paper is a result of estimated transversality with respect to stratifications of jet spaces in the approximately holomorphic category over an almost-complex manifold. The notion of asymptotic ampleness of complex vector bundles over an almost-complex manifold is also discussed, as well as applications to the construction of maps with generic singularities from compact symplectic manifolds to projective spaces.
• Refined Kato inequalities and conformal weights in Riemannian geometry
  
  • Herzlich Marc
  • Gauduchon Paul
  • Calderbank David M. J.
  Journal of Functional Analysis, Elsevier, 2000, 173 (1), pp.214-255. (10.1006/jfan.2000.3563)
  DOI : 10.1006/jfan.2000.3563
• Symplectic maps to projective spaces and symplectic invariants
  
  • Auroux Denis
  , 2000. After reviewing recent results on symplectic Lefschetz pencils and symplectic branched covers of CP^2, we describe a new construction of maps from symplectic manifolds of any dimension to CP^2 and the associated monodromy invariants. We also show that a dimensional induction process makes it possible to describe any compact symplectic manifold by a series of words in braid groups and a word in a symmetric group.
• Le théorème de spécialisation du groupe fondamental
  
  • Orgogozo Fabrice
  • Vidal Isabelle
  , 2000, pp.169--184. Soit X une courbe propre et lisse au-dessus d'un trait strictement hensélien complet S d'exposant caractéristique p. On définit une flèche de spécialisation du groupe fondamental de la fibre générique géométrique dans le groupe fondamental de la fibre spéciale. On prouve que cette flèche est surjective et induit un isomorphisme sur les plus grands quotients d'ordre premier à p. On généralise ensuite ce résultat au cas d'une courbe propre et lisse privée d'un diviseur étale D en se restreignant aux revêtements modérés le long de D. Tous ces théorèmes sont dus à A. Grothendieck et sont démontrés dans un cadre plus général dans SGA 1.
• On the infinitesimal isometries of manifolds with Killing spinors
  
  • Moroianu Andrei
  Journal of Geometry and Physics, Elsevier, 2000, 35, pp.63-74. We study the Lie algebra of infinitesimal isometries of seven-dimensional simply connected manifolds with Killing spinors. We obtain some splitting theorems for the action of this algebra on the space of Killing spinors, and as a corollary we prove that there is no infinitesimal isometry of constant length on a seven-dimensional 3-Sasakian manifold (not isometric to a space form) except the linear combinations of the Sasakian vector fields. (10.1016/S0393-0440(99)00079-0)
  DOI : 10.1016/S0393-0440(99)00079-0
• Parallel spinors and holonomy groups
  
  • Moroianu Andrei
  • Semmelmann Uwe
  Journal of Mathematical Physics, American Institute of Physics (AIP), 2000, 41, pp.2395-2402. In this paper we complete the classification of spin manifolds admitting parallel spinors, in terms of the Riemannian holonomy groups. More precisely, we show that on a given n-dimensional Riemannian manifold, spin structures with parallel spinors are in one to one correspondence with lifts to Spin_n of the Riemannian holonomy group, with fixed points on the spin representation space. In particular, we obtain the first examples of compact manifolds with two different spin structures carrying parallel spinors.