Deformations of weak $\mathbb{Q}$-Fano 3-folds

Taro Sano

Deformations of weak $\mathbb{Q}$-Fano 3-folds

Algebraic Geometry 2017-09-12 v2

Authors: Taro Sano

Abstract

We prove that a weak $\mathbb{Q}$ -Fano $3$ -fold with terminal singularities has unobstructed deformations. By using this result and computing some invariants of a terminal singularity, we provide two results on global deformation of a weak $\mathbb{Q}$ -Fano $3$ -fold. We also treat a stacky proof of the unobstructedness of deformations of a $\mathbb{Q}$ -Fano $3$ -fold.

Keywords

weak q-fano 3-fold terminal singularity unobstructed deformation global deformation stacky proof singularity invariant

Cite

@article{arxiv.1512.09209,
  title  = {Deformations of weak $\mathbb{Q}$-Fano 3-folds},
  author = {Taro Sano},
  journal= {arXiv preprint arXiv:1512.09209},
  year   = {2017}
}

Comments

21 pages. Added several propositions about infinitesimal deformations. Deleted a section about a bound of singularities on a Q-Fano 3-fold. Instead, added a new section on Q-smoothability of a weak Q-Fano 3-fold

Deformations of weak $\mathbb{Q}$-Fano 3-folds

Abstract

Keywords

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