Year: 2001
Type: article
Abstract: We construct a mirror-type correspondence that assigns variations (that is, local systems, -modules or -adic sheaves) to pairs , where is a variety and is a complex of densely filtered vector bundles over . We consider Calabi-Yau complete intersections in projective spaces. In the particular case when the complex is quasi-isomorphic to the tangent bundle on a generic Calabi-Yau complete intersection, this construction yields the variation that arises in the relative cohomology of the mirror-dual pencil. We call it the Riemann-Roch variation. The Riemann-Roch data of the divisorial sublattice in the -group can be read off the Riemann-Roch local system since it encodes the information about the Euler characteristics of all sheaves (in an essentially non-commutative way).
Source: Izvestiya Mathematics
Author: D V Osipov
Institution: Steklov Mathematical Institute
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: bronze
OpenAlex ID: W1989774940