Degenerations to unobstructed Fano Stanley-Reisner schemes
type: Item
instance of: scholarly article
title: Degenerations to unobstructed Fano Stanley-Reisner schemes
zbMATH Open document ID: 1341.14015
author: Jan Arthur Christophersen
author: Nathan Owen Ilten
published in: Mathematische Zeitschrift
publication date: 2014-10-17T00:00:00Z
full work available at URL: https://arxiv.org/abs/1102.4521
review text: Mukai represented certain Fano threefolds as complete intersections in explicitely given ambient spaces (nowadays called Mukai varieties). In the present paper, the authors construct monomial degenerations of the latter and linear sections thereof. The limits are Stanley-Reisner schemes arising from simplicial complexes being the boundary of convex deltahedra. These are exactly those 3-dimensional polytopes having regular triangles as faces. Afterwards, the view point is changed. One starts with exactly these Stanley-Reisner schemes and understands the original Mukai varieties as generic deformations of them. The authors prove that this deformation theory is unobstructed, hence the Mukai varieties degenerate to every other variety specializing to these Stanley-Reisner schemes. Among them one finds toric ones provided by representing the simplicial complexes as unimodular triangulations of lattice polytopes. Finally, the authors apply this method to linear sections of \(\mathrm{Gr}(2,n)\), too.
reviewed by: Klaus Altmann
Mathematics Subject Classification ID: 14J45
Mathematics Subject Classification ID: 13F55
Mathematics Subject Classification ID: 14D15
Mathematics Subject Classification ID: 14M25
zbMATH DE Number: 6357844
zbMATH Keywords: Fano varieties
zbMATH Keywords: toric degenerations
zbMATH Keywords: deltahedra
zbMATH Keywords: Stanley-Reisner rings
zbMATH Keywords: obstructions
MaRDI profile type: Publication
OpenAlex ID: W2076195308
arXiv ID: 1102.4521
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DOI: 10.1007/S00209-014-1309-3
description: scientific article; zbMATH DE number 6357844