Finiteness for self-dual classes in integral variations of Hodge structure

Abstract

We generalize the finiteness theorem for the locus of Hodge classes with fixed self-intersection number, due to Cattani, Deligne, and Kaplan, from Hodge classes to self-dual classes. The proof uses the definability of period mappings in the o-minimal structure ${\mathbb{R}}_{\mathrm{an},\exp }$.

v3: final version

References in corpus (4)

• Les Houches Lectures on Constructing String Vacua
• On the Geometry of Moduli Space of Polarized Calabi-Yau manifolds
• Ergodic complex structures on hyperkahler manifolds: an erratum
• Definability of mixed period maps

Cited by in corpus (4)

• Finiteness and the Emergence of Dualities
• Asymptotic safety, quantum gravity, and the swampland: a conceptual assessment
• Flux vacua in type IIB compactifications on orbifolds: their finiteness and minimal string coupling
• Tame Complexity of Effective Field Theories in the Quantum Gravity Landscape