Gorenstein spherical Fano varieties

Gagliardi, Giuliano; Hofscheier, Johannes

Abstract

We obtain a combinatorial description of Gorenstein spherical Fano varieties in terms of certain polytopes, generalizing the combinatorial description of Gorenstein toric Fano varieties by reflexive polytopes and its extension to Gorenstein horospherical Fano varieties due to Pasquier. Using this description, we show that the rank of the Picard group of an arbitrary d-dimensional Q-factorial Gorenstein spherical Fano variety is bounded by 2d. This paper also contains an overview of the description of the natural representative of the anticanonical divisor class of a spherical variety due to Brion.

Citation

Gagliardi, G., & Hofscheier, J. (2015). Gorenstein spherical Fano varieties. Geometriae Dedicata, 178(1), 111-133. https://doi.org/10.1007/s10711-015-0047-y

• Journal Article Type: Article
• Acceptance Date: Jan 19, 2015
• Online Publication Date: Feb 11, 2015
• Publication Date: 2015-10
• Deposit Date: Nov 14, 2019
• Publicly Available Date: Nov 14, 2019
• Journal: Geometriae Dedicata
• Print ISSN: 0046-5755
• Electronic ISSN: 1572-9168
• Publisher: Springer Verlag
• Peer Reviewed: Peer Reviewed
• Volume: 178
• Issue: 1
• Pages: 111-133
• DOI: https://doi.org/10.1007/s10711-015-0047-y
• Keywords: Geometry and Topology
• Public URL: https://nottingham-repository.worktribe.com/output/3281463
• Publisher URL: https://link.springer.com/article/10.1007%2Fs10711-015-0047-y
• Additional Information: This is a post-peer-review, pre-copyedit version of an article published in Geometriae Dedicata. The final authenticated version is available online at: http://dx.doi.org/10.1007/s10711-015-0047-y
• Contract Date: Nov 14, 2019