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We also develop an example for a related extremal problem. Esser constructed a klt Calabi-Yau variety which conjecturally has the smallest mld in each dimension (for example, mld $1/13$ in dimension 2 and $1/311$ in dimension 3). However, the example was only worked out completely in dimensions at most 18. We now prove the desired properties of Esser's example in all dimensions (in particular, determining its mld).
| Comments: | 29 pages; v4: the paper has been published and is left unchanged, but Conjecture 7.4 has been disproved by Jihao Liu (this https URL). Namely, the klt Calabi-Yau variety of large index constructed by Esser-Totaro-Wang has smaller-than-expected index in dimension 159 |
| Subjects: | Algebraic Geometry (math.AG) |
| MSC classes: | 14J40 (Primary) 14B05, 14J32 (Secondary) |
| Cite as: | arXiv:2308.08034 [math.AG] |
| (or arXiv:2308.08034v4 [math.AG] for this version) | |
| https://doi.org/10.48550/arXiv.2308.08034 arXiv-issued DOI via DataCite |
From: Burt Totaro [view email]
[v1]
Tue, 15 Aug 2023 20:50:29 UTC (23 KB)
[v2]
Sat, 30 Dec 2023 01:50:53 UTC (23 KB)
[v3]
Tue, 7 May 2024 00:21:36 UTC (24 KB)
[v4]
Fri, 22 May 2026 18:22:28 UTC (24 KB)
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