arXiv 0809.16992008-09-10math.AG

Exceptional Loci on $\bar M_{0,n}$ and Hypergraph Curves

Ana-Maria Castravet, Jenia Tevelev

备注：: 39 pages

英文摘要：

We give a myriad of examples of extremal divisors, rigid curves, and birational morphisms with unexpected properties for the Grothendieck--Knudsen moduli space $\bar M_{0,n}$ of stable rational curves. The basic tool is an isomorphism between $M_{0,n}$ and the Brill--Noether locus of a very special reducible curve corresponding to a hypergraph.

机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。

阅读原文

阅读 PDF ↗

arXiv 页面 ↗HTML 原文 ↗

本文内容

英文摘要相关论文

机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。

继续探索

相关论文

F吹胀的例外极子与G-希尔伯特方案

Exceptional loci of F-blowups and $G$-Hilbert schemes

Instituto de Ingeniería y Tecnología, UACJ（乌斯帕塔技术工程研究所）；The University of Osaka（大阪大学）；Kavli Institute for the Physics and Mathematics of the Universe, The University of Tokyo（东京大学宇宙物理与数学研究所）

研究F吹胀正常分形变的例外极子，通过组合数据给出素除子中心维数公式，并探讨F吹胀与三维终端奇点和canonical奇点的关联。

2026-04-26math.AG

Exceptional loci in Lefschetz theory

Let $ϕ:X\rightarrow \mathbb{P}^n$ be a morphism of varieties. Given a hyperplane $H$ in $\mathbb{P}^n$, there is a Gysin map from the compactly supported cohomology of $ϕ^{-1}(H)$ to that of $X$. We give conditions on the degree of the cohomology under which this map is an isomorphism for all but a low-dimensional set of hyperplanes, generalizing results due to Skorobogatov, Benoist, and Poonen-Slavov. Our argument is based on Beilinson's theory of singular supports for étale sheaves.

2021-06-18math.AG

代数曲面中的例外集

Exceptional loci in algebraic surfaces

Università Roma Tre（罗马三大学）

研究log一般类型的曲面(S,B)的代数例外集，当B至少有三个不可约分量时，证明其通常有限或为空。

2026-03-26math.AGmath.NT

Some examples of exceptional loci in Vojta Conjecture

In this short note we discuss the exceptional locus for the Lang-Vojta's conjecture in the case of the complement of two completely reducible hyperplane sections in a cubic surface. Using elementary methods, we show that generically the exceptional set is the union of the remaining 21 lines in the surface. We also describe examples in which the exceptional set is strictly larger.

2021-10-29math.AGmath.NT

诺特概形上的相对增广基轨迹

Relative augmented base loci on noetherian schemes

本文在诺特概形上证明可逆层的相对增广基轨迹等于相对例外轨迹，并给出推广 Keel 结果的半丰富性判据。

2023-08-07math.AG

例外轨迹与满足 $\bar{c}_1^2 - \bar{c}_2 > 0$ 的平面曲线补集的双曲性

Exceptional Loci and Hyperbolicity of Complements of Plane Curves with $\bar{c}_1^2 - \bar{c}_2 > 0$

Roma Tre University（罗马第三大学）

本文证明满足特定次数条件的一般平面曲线，其代数例外集为空，进而得出满足 $\bar{c}_1^2 - \bar{c}_2 > 0$ 的平面曲线补集是 Kobayashi 双曲的。

2026-09-30math.AG

更多相关论文收起更多论文

Birational geometry of the Mukai system of rank two and genus two

Using the techniques of Bayer--Macrì, we determine the walls in the movable cone of the Mukai system of rank two for a general K3 surface $S$ of genus two. We study the (essentially unique) birational map to $S^{[5]}$ and decompose it into a sequence of flops. We give an interpretation of the exceptional loci in terms of Brill--Noether loci.

2020-09-01math.AG

Birational geometry of Beauville-Mukai systems I: the rank three and genus two case

We study wall-crossing for the Beauville-Mukai system of rank three on a general genus two K3 surface. We show that such a system is related to the Hilbert scheme of ten points on the surface by a sequence of flops, whose exceptional loci can be described as Brill-Noether loci. We also obtain Brill-Noether type results for sheaves in the Beauville-Mukai system.

2022-07-26math.AG

Frobenius distribution for pairs of elliptic curves and exceptional isogenies

Let E and E' be two elliptic curves over a number field. We prove that the reductions of E and E' at a finite place p are geometrically isogenous for infinitely many p, and draw consequences for the existence of supersingular primes. This result is an analogue for distributions of Frobenius traces of known results on the density of Noether-Lefschetz loci in Hodge theory. The proof relies on dynamical properties of the Hecke correspondences on the modular curve.

2014-11-11math.AGmath.NT

The augmented base locus of real divisors over arbitrary fields

We show that the augmented base locus coincides with the exceptional locus (i.e. null locus) for any nef $\mathbb{R}$-Cartier divisor on any scheme projective over a field (of any characteristic). Next we prove a semi-ampleness criterion in terms of the augmented base locus generalizing a result of Keel. We also study nef divisors with positive top intersection number, and discuss some problems related to augmented base loci of log divisors.

2013-12-01math.AG

Rigid divisors on surfaces

We study effective divisors $D$ on surfaces with $H^0(\mathcal O_D)=k$ and $H^1(\mathcal O_D)=H^0(\mathcal O_D(D))=0$. We give a numerical criterion for such divisors, following a general investigation of negativity, rigidity and connectivity properties. Examples include exceptional loci of rational singularities, and spherelike divisors.

2020-03-21math.AG

Contraction centers in families of hyperkahler manifolds

We study the exceptional loci of birational (bimeromorphic) contractions of a hyperkähler manifold $M$. Such a contraction locus is the union of all minimal rational curves in a collection of cohomology classes which are orthogonal to a wall of the Kähler cone. Homology classes which can possibly be orthogonal to a wall of the Kähler cone of some deformation of $M$ are called MBM classes. We prove that all MBM classes of type (1,1) can be represented by rational curves, called MBM curves. All MBM curves can be contracted on an appropriate birational model of $M$, unless $b_2(M) \leq 5$. When $…

2021-06-29math.AG