Hodge theory of Log Singular Loci

• Applicant: Professor Dr. Helge Ruddat
• Subject Area: Mathematics
• Term: Funded in 2013
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 241231364

• Final Report Year: 2014

Final Report Abstract

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.

Publications

• 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.
  (See online at https://doi.org/10.1090/jag/666)