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| Format: | Preprint |
| Published: |
2016
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/1701.00027 |
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| _version_ | 1866914894704541696 |
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| author | Muratore, Giosuè Emanuele |
| author_facet | Muratore, Giosuè Emanuele |
| contents | The 2-Fano varieties, defined by De Jong and Starr, satisfy some higher dimensional analogous properties of Fano varieties. We propose a definition of (weak) $k$-Fano variety and conjecture the polyhedrality of the cone of pseudoeffective $k$-cycles for those varieties in analogy with the case $k=1$. Then, we calculate some Betti numbers of a large class of $k$-Fano varieties to prove some special case of the conjecture. In particular, the conjecture is true for all 2-Fano varieties of index $\ge n-2$, and also we complete the classification of weak 2-Fano varieties of Araujo and Castravet. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1701_00027 |
| institution | arXiv |
| publishDate | 2016 |
| record_format | arxiv |
| spellingShingle | Betti numbers and pseudoeffective cones in 2-Fano varieties Muratore, Giosuè Emanuele Algebraic Geometry 14J45, 14M15 The 2-Fano varieties, defined by De Jong and Starr, satisfy some higher dimensional analogous properties of Fano varieties. We propose a definition of (weak) $k$-Fano variety and conjecture the polyhedrality of the cone of pseudoeffective $k$-cycles for those varieties in analogy with the case $k=1$. Then, we calculate some Betti numbers of a large class of $k$-Fano varieties to prove some special case of the conjecture. In particular, the conjecture is true for all 2-Fano varieties of index $\ge n-2$, and also we complete the classification of weak 2-Fano varieties of Araujo and Castravet. |
| title | Betti numbers and pseudoeffective cones in 2-Fano varieties |
| topic | Algebraic Geometry 14J45, 14M15 |
| url | https://arxiv.org/abs/1701.00027 |