SMF

Compactifications of moduli spaces inspired by mirror symetry

Compactifications of moduli spaces inspired by mirror symetry

D. MORRISON
  • Année : 1993
  • Tome : 218
  • Format : Papier, Électronique
  • Langue de l'ouvrage :
    Anglais
  • Class. Math. : 14J30
  • Pages : 243-271
  • DOI : 10.24033/ast.248

We study moduli spaces of nonlinear sigma-models on Calabi-Yau manifolds, using the one-loop semi jcal approximation. The data being parameterized includes a choice of complex structure on the manifold, as well as some “extra structure” described by means of es in H$^2$. We formulate a simple and compelling conjecture about the action of the automorphism group on the Kähler cone, which would enable the construction of a partial compactification of the moduli space using Looijenga's “semi-toric” method. We then explore the implications which this construction has concerning the properties of the moduli space of complex structures on a “mirror partner” of the original Calabi-Yau manifold.

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