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
ISSN1056-3911
EISSN1534-7486
卷号30期号:1页码:1-56
DOI10.1090/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.
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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
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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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