2 n2-inequality for cA1 points and applications to birational rigidity

IF 1.3 1区 数学 Q1 MATHEMATICS Compositio Mathematica Pub Date : 2024-05-29 DOI:10.1112/s0010437x24007164
Igor Krylov, Takuzo Okada, Erik Paemurru, Jihun Park
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引用次数: 0

Abstract

The Abstract Image$4 n^2$-inequality for smooth points plays an important role in the proofs of birational (super)rigidity. The main aim of this paper is to generalize such an inequality to terminal singular points of type Abstract Image$cA_1$, and obtain a Abstract Image$2 n^2$-inequality for Abstract Image$cA_1$ points. As applications, we prove birational (super)rigidity of sextic double solids, many other prime Fano 3-fold weighted complete intersections, and del Pezzo fibrations of degree Abstract Image$1$ over Abstract Image$\mathbb {P}^1$ satisfying the Abstract Image$K^2$-condition, all of which have at most terminal Abstract Image$cA_1$ singularities and terminal quotient singularities. These give first examples of birationally (super)rigid Fano 3-folds and del Pezzo fibrations admitting a Abstract Image$cA_1$ point which is not an ordinary double point.

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2 cA1点的n2-不等式及其在双刚性中的应用
光滑点的 $4 n^2$ 不等式在双(超)刚性证明中起着重要作用。本文的主要目的是将这种不等式推广到 $cA_1$ 类型的末端奇异点,并获得 $cA_1$ 点的 $2 n^2$ 不等式。作为应用,我们证明了六元双实体、许多其他素数法诺 3 折叠加权完全交集以及满足 $K^2$ 条件的 $\mathbb {P}^1$ 上 1$ 度的 del Pezzo 纤 维的双向(超)刚性,所有这些都最多有末端的 $cA_1$ 奇点和末端的商奇点。这些给出了双向(超)刚性法诺 3 折叠和德尔佩佐纤维的第一个例子,其中的 $cA_1$ 点不是普通的双点。
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来源期刊
Compositio Mathematica
Compositio Mathematica 数学-数学
CiteScore
2.10
自引率
0.00%
发文量
62
审稿时长
6-12 weeks
期刊介绍: Compositio Mathematica is a prestigious, well-established journal publishing first-class research papers that traditionally focus on the mainstream of pure mathematics. Compositio Mathematica has a broad scope which includes the fields of algebra, number theory, topology, algebraic and differential geometry and global analysis. Papers on other topics are welcome if they are of broad interest. All contributions are required to meet high standards of quality and originality. The Journal has an international editorial board reflected in the journal content.
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