Publications

1996

• Formes harmoniques en présence de spineurs de Killing kähleriens
  
  • Moroianu Andrei
  Comptes rendus de l'Académie des sciences. Série I, Mathématique, Elsevier, 1996, 322, pp.679-684. We show that the Clifford product between an effective harmonic form and a Kählerian Killing spinor vanishes, which is the Kählerian analogue of Hijazi's result concerning Riemannian Killing spinors. As a corollary, we prove that there is no parallel effective $(p,p)$-form $(p>0)$ on Kähler-Einstein manifolds admitting a complex contact structure.
• Structures de Weyl admettant des spineurs parallèles
  
  • Moroianu Andrei
  Bulletin de la société mathématique de France, Société Mathématique de France, 1996, 124, pp.685-695. We prove that given a Weyl structure $D$ on a spin manifold $(M^n,g)$, the existence of a non-zero $D$-parallel spinor on $M$ implies that $D$ is closed for $n\ne4$. The same statement is true for $n=4$ if $M$ is compact. We give non-compact examples of 4-manifolds admitting parallel spinors with respect to non-closed Weyl structures.
• Moduli of pre-$\cal D$-modules, perverse sheaves and the Riemann-Hilbert morphism -I
  
  • Nitsure Nitin
  • Sabbah Claude
  Mathematische Annalen, Springer Verlag, 1996, 306 (1), pp.47-73. We construct a moduli scheme for semistable pre-$\D$-modules with prescribed singularities and numerical data on a smooth projective variety. These pre-$\D$-modules are to be viewed as regular holonomic $\D$-modules with 'level structure'. We also construct a moduli scheme for perverse sheaves on the variety with prescribed singularities and other numerical data, and represent the de Rham functor (which gives the Riemann-Hilbert correspondence) by an analytic morphism between the two moduli schemes. (10.1007/BF01445242)
  DOI : 10.1007/BF01445242
• Sur les valeurs propres de l'opérateur de Dirac des variétés 3-sasakiennes
  
  • Moroianu Andrei
  Stud. Cerc. Mat., 1996, 48, pp.85-88. We find explicit eigenvalues for the Dirac operator on compact 3-Sasakian manifolds and give lower bounds on their multiplicities.
• Vanishing conditions for the simplicial volume of complex varieties
  
  • Ville Marina
  Proceedings of the American Mathematical Society, American Mathematical Society, 1996, 124 (04), pp.987-994. Gromov has dfined a notion of simplicial volume: it is a topological invariant for compact manifolds which is closely related to the fundamental group. We investigate here the relevance of this notion in the realm of complex varieties. (10.1090/S0002-9939-96-02652-4)
  DOI : 10.1090/S0002-9939-96-02652-4
• Kählerian Killing Spinors, Complex Contact Structures and Twistor Spaces
  
  • Moroianu Andrei
  • Semmelmann Uwe
  Comptes rendus de l'Académie des sciences. Série I, Mathématique, Elsevier, 1996, 323, pp.57-61. On utilise nos résultats récents pour montrer l'qéuivalence des trois notions du titre sous certaines conditions. On obtient ensuite des conséquences sur les variétés de Sasaki, les structures presque complexes de contact, et les $k$-structures complexes de contact.