## Advances in Theoretical and Mathematical Physics: ATMP., Volume 6, Pages 403-793 |

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### Contents

Toric morphisms and fibrations of toric CalabiYau hypersurfaces | 457 |

Isolated horizons in 2 + 1 gravity | 507 |

HyperKahler manifolds and birational transformations | 557 |

6 other sections not shown

### Common terms and phrases

action algebra associated asymptotic background birational black hole boundary conditions brane Calabi-Yau threefold Chern-Simons Chern-Simons theory closed string closed string vertex coefficients computation cones configuration constant coordinates corresponding D-brane defined denote dimensional disc discussed duality equations F5-brane fiber fibration finite fixed gauge invariant gauge invariant operators ghost given H-SLag Hamiltonian holomorphic homology hypersurfaces induced infinity instanton integral irreducible component isolated horizon isomorphic Kaluza-Klein reductions Killing spinors Killing vector Lagrangian lattice Lemma line bundle locus M-theory M2-brane manifold Math metric Mirror Symmetry moduli space non-expanding horizon null normal obtained open string orbit OSFT parameters Phys polytope rational curve reparametrization restriction rotation singular smooth solution spacelike spacetime string field theory string vertex operators subalgebra supergravity supersymmetry surface tachyon tensor topological toric geometry toric morphism toric variety transformation Vafa vanishes vector field VSFT weakly isolated horizon zero