COHOMOLOGICAL RIGIDITY FOR TORIC FANO MANIFOLDS OF SMALL DIMENSIONS OR LARGE PICARD NUMBERS

Higashitani, Akihiro; Kurimoto, Kazuki; Masuda, Mikiya

Osaka Journal of Mathematics, 2022, 59(1), 177-215

Number of Access:406（2025-10-23 12:06 Counts）

Identifier to cite or link to this item: https://doi.org/10.18910/86340

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Title
COHOMOLOGICAL RIGIDITY FOR TORIC FANO MANIFOLDS OF SMALL DIMENSIONS OR LARGE PICARD NUMBERS
Creator
NRID
1000060723385 1000060723385
researchmap permalink
7000011220 7000011220
Scopus Author ID
36105210100 36105210100
ORCID
0000-0002-3824-425X 0000-0002-3824-425X
CreatorName
Higashitani, Akihiro
CreatorName
Kurimoto, Kazuki
NRID
1000000143371 1000000143371
CreatorName
Masuda, Mikiya
Abstract
The cohomological rigidity problem for toric manifolds asks whether toric manifolds are diffeomorphic (or homeomorphic) if their integral cohomology rings are isomorphic. Many affirmative partial solutions to the problem have been obtained and no counterexample is known. In this paper, we study the diffeomorphism classification of toric Fano d-folds with d = 3, 4 or with Picard number ≥ 2d − 2. In particular, we show that those manifolds except for two toric Fano 4-folds are diffeomorphic if their integral cohomology rings are isomorphic. The exceptional two toric Fano 4-folds (their ID numbers are 50 and 57 on a list of Øbro) have isomorphic cohomology rings and their total Pontryagin classes are preserved under an isomorphism between their cohomology rings, but we do not know whether they are diffeomorphic or homeomorphic.
Publisher
Osaka University and Osaka City University, Departments of Mathematics
Source Title
Osaka Journal of Mathematics
Volume (Issue)
59(1)
Page
177-215
Date of Issued
2022-01
Language
English
Handle URL
https://hdl.handle.net/11094/86340
DOI
https://doi.org/10.18910/86340
PISSN
00306126
NCID
AA00765910
Access Rights
open access
oaire:version
Version of Record
Category
紀要論文 Departmental Bulletin Paper
Osaka Journal of Mathematics / Volume 59, Number 1 （2022-1）