Four-Dimensional Projective Orbifold Hypersurfaces

被引：14

作者：

Brown, Gavin ^{[1
]}

Kasprzyk, Alexander ^{[2
]}

机构：

[1] Univ Warwick, Math Inst, Coventry CV4 7AL, W Midlands, England

[2] Univ Nottingham, Sch Math Sci, Nottingham NG7 2RD, England

来源：

EXPERIMENTAL MATHEMATICS | 2016年 / 25卷 / 02期

基金：

欧洲研究理事会; 英国工程与自然科学研究理事会;

关键词：

Fano; Calabi-Yau; threefold; fourfold; orbifold; weighted hypersurface; FANO; 3-FOLDS; CLASSIFICATION; SINGULARITIES; VARIETIES;

D O I：

10.1080/10586458.2015.1054054

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We classify four-dimensional quasismooth weighted hypersurfaces with small canonical class and verify a conjecture of Johnson and Kollar on infinite series of quasismooth hypersurfaces with anticanonical hyperplane section in the case of fourfolds. By considering the quotient singularities that arise, we classify those weighted hypersurfaces that are canonical, Calabi-Yau and Fano fourfolds. We also consider other classes of hypersurfaces, including Fano hypersurfaces of index greater than 1 in dimensions 3 and 4.

引用

页码：176 / 193

页数：18

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