The unobstructedness theorem for pairs of a log Calabi–Yau log toroidal family and a line bundle allows us to construct polarized formal smoothings in the projective case. The polarization then allows us to algebraize the formal smoothing into an algebraic smoothing over the power series ring. This situation has already been discussed in the introduction, and in this chapter, we complement the material with further considerations.

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Algebraic Deformations

  • Simon Felten

摘要

The unobstructedness theorem for pairs of a log Calabi–Yau log toroidal family and a line bundle allows us to construct polarized formal smoothings in the projective case. The polarization then allows us to algebraize the formal smoothing into an algebraic smoothing over the power series ring. This situation has already been discussed in the introduction, and in this chapter, we complement the material with further considerations.