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THE GEOMETRY OF DEGENERATIONS OF HILBERT SCHEMES OF POINTS | |
Gulbrandsen, Martin G.1; Halle, Lars H.2; Hulek, Klaus3; Zhang, Ziyu3,4 | |
2021 | |
发表期刊 | JOURNAL OF ALGEBRAIC GEOMETRY |
ISSN | 1056-3911 |
EISSN | 1534-7486 |
卷号 | 30期号:1页码:1-56 |
DOI | 10.1090/jag/765 |
摘要 | Given a strict simple degeneration f : X -> C the first three authors previously constructed a degeneration I-X/C(n) -> C of the relative degree n Hilbert scheme of 0-dimensional subschemes. In this paper we investigate the geometry of this degeneration, in particular when the fibre dimension of f is at most 2. In this case we show that I-X/C(n) -> C is a dlt model. This is even a good minimal dlt model if f:X -> C has this property. We compute the dual complex of the central fibre (I-X/C(n))(0) and relate this to the essential skeleton of the generic fibre. For a type II degeneration of K3 surfaces we show that the stack I-X/C(n) -> C carries a nowhere degenerate relative logarithmic 2-form. Finally we discuss the relationship of our degeneration with the constructions of Nagai. |
URL | 查看原文 |
收录类别 | SCI ; SCIE |
语种 | 英语 |
WOS研究方向 | Mathematics |
WOS类目 | Mathematics |
WOS记录号 | WOS:000625298600001 |
出版者 | UNIV PRESS INC |
WOS关键词 | SYMMETRIC PRODUCTS ; ESSENTIAL SKELETON ; MODULI |
原始文献类型 | Article |
引用统计 | |
文献类型 | 期刊论文 |
条目标识符 | https://kms.shanghaitech.edu.cn/handle/2MSLDSTB/125908 |
专题 | 数学科学研究所_PI研究组(P)_张子宇组 |
通讯作者 | Gulbrandsen, Martin G. |
作者单位 | 1.Univ Stavanger, Dept Math & Nat Sci, N-4036 Stavanger, Norway; 2.Univ Copenhagen, Dept Math Sci, Univ Pk 5, DK-2100 Copenhagen, Denmark; 3.Inst Algebra Geometrie, Welfen Garten 1, D-30167 Hannover, Germany; 4.ShanghaiTech Univ, Inst Math Sci, 393 Middle Huaxia Rd, Shanghai 201210, Peoples R China |
推荐引用方式 GB/T 7714 | Gulbrandsen, Martin G.,Halle, Lars H.,Hulek, Klaus,et al. THE GEOMETRY OF DEGENERATIONS OF HILBERT SCHEMES OF POINTS[J]. JOURNAL OF ALGEBRAIC GEOMETRY,2021,30(1):1-56. |
APA | Gulbrandsen, Martin G.,Halle, Lars H.,Hulek, Klaus,&Zhang, Ziyu.(2021).THE GEOMETRY OF DEGENERATIONS OF HILBERT SCHEMES OF POINTS.JOURNAL OF ALGEBRAIC GEOMETRY,30(1),1-56. |
MLA | Gulbrandsen, Martin G.,et al."THE GEOMETRY OF DEGENERATIONS OF HILBERT SCHEMES OF POINTS".JOURNAL OF ALGEBRAIC GEOMETRY 30.1(2021):1-56. |
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