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On classifying the divisor involutions in Calabi-Yau threefolds. (English) Zbl 1342.81425
Summary: In order to support the odd moduli in models of (type IIB) string compactification, we classify the Calabi-Yau threefolds with \(h^{1,1}\leq 4\) which exhibit pairs of identical divisors, with different line-bundle charges, mapping to each other under possible divisor exchange involutions. For this purpose, the divisors of interest are identified as completely rigid surface, Wilson surface, \(K3\) surface and some other deformation surfaces. Subsequently, various possible exchange involutions are examined under the symmetry of Stanley-Reisner Ideal. In addition, we search for the Calabi-Yau theefolds which contain a divisor with several disjoint components. Under certain reflection involution, such spaces also have nontrivial odd components in \((1,1)\)-cohomology class. String compactifications on such Calabi-Yau orientifolds with non-zero \(h^{1,1}-(CY3/\sigma)\) could be promising for concrete model building in both particle physics and cosmology. In the spirit of using such Calabi-Yau orientifolds in the context of large volume scenario, we also present some concrete examples of (strong/weak) swiss-cheese type volume form.

MSC:
81T30 String and superstring theories; other extended objects (e.g., branes) in quantum field theory
14J32 Calabi-Yau manifolds (algebro-geometric aspects)
14M25 Toric varieties, Newton polyhedra, Okounkov bodies
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