Hodge-Theorie log singulärer Loci

• Antragsteller: Professor Dr. Helge Ruddat
• Fachliche Zuordnung: Mathematik
• Förderung: Förderung in 2013
• Projektkennung: Deutsche Forschungsgemeinschaft (DFG) - Projektnummer 241231364

• Erstellungsjahr: 2014

Zusammenfassung der Projektergebnisse

The project establishes a subtle connection between mirror symmetry for Calabi-Yau threefolds and that of curves of higher genus. The linking structure is what we call a perverse curve. We show how one obtains such from Calabi-Yau threefolds in the Batyrev mirror construction by constructing a perverse sheaf supported on the log singular locus of the central fibre of the degeneration to infinity. We prove that the Hodge diamonds of a pair of perverse curves obtained from mirror dual families are themselves mirror dual in the sense of that they have reflected Hodge diamonds.

Projektbezogene Publikationen (Auswahl)

• Perverse Curves and Mirror Symmetry, last revised 14 Aug 2014 (this version, v2), 24 pages, 6 figures, to appear in: Journal of Algebraic Geometry.
  Ruddat, H.