Toroidal crossings and logarithmic structures

@article{Schrer2002ToroidalCA,
  title={Toroidal crossings and logarithmic structures},
  author={S. Schr{\"o}er and Bernd S Siebert},
  journal={Advances in Mathematics},
  year={2002},
  volume={202},
  pages={189-231}
}
  • S. Schröer, Bernd S Siebert
  • Published 2002
  • Mathematics
  • Advances in Mathematics
  • Abstract We generalize Friedman's notion of d-semistability, which is a necessary condition for spaces with normal crossings to admit smoothings with regular total space. Our generalization deals with spaces that locally look like the boundary divisor in Gorenstein toroidal embeddings. In this situation, we replace d-semistability by the existence of global log structures for a given gerbe of local log structures. This leads to cohomological descriptions for the obstructions, existence, and… CONTINUE READING
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    References

    SHOWING 1-10 OF 58 REFERENCES
    Affine manifolds, log structures, and mirror symmetry
    • 76
    • PDF
    Universal log structures on semi-stable varieties
    • 26
    • PDF
    The bigger Brauer group is really big
    • 9
    • PDF
    Log smooth deformation theory
    • 112
    • PDF
    Nonnormal Del Pezzo Surfaces
    • NONNORMAL DEL PEZZO
    • 1994
    • 34
    On the joins of hensel rings
    • 104
    LOGARITHMIC GEOMETRY AND ALGEBRAIC STACKS
    • 134
    • PDF
    Hilbert functions of graded algebras
    • 710
    • Highly Influential
    • PDF
    There are enough Azumaya algebras on surfaces
    • 23
    • PDF