二次曲线的完全相交和具有共同专门化的Segre变种的完全相交

IF 0.9 3区数学 Q2 MATHEMATICS

Documenta Mathematica Pub Date : 2021-01-01 DOI:10.4171/dm/818

C. Peters, H. Sterk

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引用次数: 0

摘要

．研究了Segre嵌入积p1 × kp →p2 k +1中二次曲面的完全相交曲面和完全相交曲面是否属于同一Hilbert格式。对于k = 2有一个经典的例子;它来自射影5空间中的K3曲面，这些曲面退化为Segre三重曲面上的超曲面。我们证明，当k≥3时，只剩下一个例子。结果表明，它的(连通的)希尔伯特格式至少有两个不可约的分量。我们研究了相应的局部模

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Complete intersections of quadrics and complete intersections on Segre varieties with common specializations

. We investigate whether surfaces that are complete intersections of quadrics and complete intersection surfaces in the Segre embedded product P 1 × P k ֒ → P 2 k +1 can belong to the same Hilbert scheme. For k = 2 there is a classical example; it comes from K3 surfaces in projective 5-space that degenerate into a hypersurface on the Segre threefold. We show that for k ≥ 3 there is only one more example. It turns out that its (connected) Hilbert scheme has at least two irreducible components. We investigate the corresponding local moduli

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来源期刊

Documenta Mathematica 数学-数学

CiteScore

1.60

自引率

11.10%

发文量

审稿时长

>12 weeks

期刊介绍： DOCUMENTA MATHEMATICA is open to all mathematical fields und internationally oriented Documenta Mathematica publishes excellent and carefully refereed articles of general interest, which preferably should rely only on refereed sources and references.