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arXiv · 2211.14089

From formal smoothings to geometric smoothings

Alessandro Nobile
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Abstract

Let X be a projective, equidimensional, singular scheme over an algebraically closed field. Then the existence of a geometric smoothing (i.e. a family of deformations of X over a smooth base curve whose generic fibre is smooth) implies the existence of a formal smoothing as defined by Tziolas. In this paper we address the reverse question giving sufficient conditions on X that guarantee the converse, i.e. formal smoothability implies geometric smoothability. This is useful in light of Tziolas' results giving sufficient criteria for the existence of formal smoothings.

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Alessandro Nobile. 2022-11-25. From formal smoothings to geometric smoothings. https://arxiv.org/abs/2211.14089

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