An inductive approach to generalized abundance using nef reduction
We use the canonical bundle formula for parabolic fibrations to give an inductive approach to the generalized abundance conjecture using nef reduction. In particular, we observe that generalized abundance holds for a klt pair $(X,B)$ if the nef dimension $n(K_X+B+L)=2$ and $K_X+B \ge 0$ or $n(K_X+B+...
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| Language: | English |
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Académie des sciences
2023-01-01
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| Series: | Comptes Rendus. Mathématique |
| Online Access: | https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.420/ |
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| author | Chaudhuri, Priyankur |
| author_facet | Chaudhuri, Priyankur |
| author_sort | Chaudhuri, Priyankur |
| collection | DOAJ |
| description | We use the canonical bundle formula for parabolic fibrations to give an inductive approach to the generalized abundance conjecture using nef reduction. In particular, we observe that generalized abundance holds for a klt pair $(X,B)$ if the nef dimension $n(K_X+B+L)=2$ and $K_X+B \ge 0$ or $n(K_X+B+L)=3$ and $\kappa (K_X+B)>0$. |
| format | Article |
| id | doaj-art-005ab9520641472d9616b447d7018595 |
| institution | Kabale University |
| issn | 1778-3569 |
| language | English |
| publishDate | 2023-01-01 |
| publisher | Académie des sciences |
| record_format | Article |
| series | Comptes Rendus. Mathématique |
| spelling | doaj-art-005ab9520641472d9616b447d70185952025-02-07T11:06:07ZengAcadémie des sciencesComptes Rendus. Mathématique1778-35692023-01-01361G141742110.5802/crmath.42010.5802/crmath.420An inductive approach to generalized abundance using nef reductionChaudhuri, Priyankur0Department of Mathematics, University of Maryland, College Park, MD 20742, USAWe use the canonical bundle formula for parabolic fibrations to give an inductive approach to the generalized abundance conjecture using nef reduction. In particular, we observe that generalized abundance holds for a klt pair $(X,B)$ if the nef dimension $n(K_X+B+L)=2$ and $K_X+B \ge 0$ or $n(K_X+B+L)=3$ and $\kappa (K_X+B)>0$.https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.420/ |
| spellingShingle | Chaudhuri, Priyankur An inductive approach to generalized abundance using nef reduction Comptes Rendus. Mathématique |
| title | An inductive approach to generalized abundance using nef reduction |
| title_full | An inductive approach to generalized abundance using nef reduction |
| title_fullStr | An inductive approach to generalized abundance using nef reduction |
| title_full_unstemmed | An inductive approach to generalized abundance using nef reduction |
| title_short | An inductive approach to generalized abundance using nef reduction |
| title_sort | inductive approach to generalized abundance using nef reduction |
| url | https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.420/ |
| work_keys_str_mv | AT chaudhuripriyankur aninductiveapproachtogeneralizedabundanceusingnefreduction AT chaudhuripriyankur inductiveapproachtogeneralizedabundanceusingnefreduction |