32 research outputs found
Formality of derived intersections
We study derived intersections of smooth analytic cycles, and provide in some
cases necessary and sufficient conditions for this intersection be formal. In
particular, if X is a complex submanifold of a complex manifold Y, we prove
that X can be quantized if and only if the derived intersection of XxX and
\Delta_Y is formal in D(XxX).Comment: A mistake has been corrected in Section
On a conjecture of Kashiwara relating Chern and Euler classes of O-modules
In this note we prove a conjecture of Kashiwara, which states that the Euler
class of a coherent analytic sheaf F on a complex manifold X is the product of
the Chern character of F with the Todd class of X. As a corollary, we obtain a
functorial proof of the Grothendieck-Riemann-Roch theorem in Hodge cohomology
for complex manifolds.Comment: Final versio
Infinitesimal deformations of rational surface automorphisms
If is a rational surface without nonzero holomorphic vector field and
is an automorphism of , we study in several examples the Zariski tangent
space of the local deformation space of the pair .Comment: Final versio
Variation of the holomorphic determinant bundle
In this paper, we prove that the Grothendieck-Riemann-Roch formula in Deligne
cohomology computing the determinant of the cohomology of a holomorphic vector
bundle on the fibers of a proper submersion between abstract complex manifolds
is invariant by deformation of the bundle.Comment: Comments are welcom
Chern classes in Deligne cohomology for coherent analytic sheaves
In this article, we construct Chern classes in rational Deligne cohomology
for coherent sheaves on a smooth complex compact manifold. We prove that these
classes verify the functoriality property under pullbacks, the Whitney formula
and the Grothendieck-Riemann-Roch theorem for projective morphisms between
smooth complex compact manifolds.Comment: Minor change