Searcharxiv⌕ Search
Home/Archive/arXiv

arXiv · alg-geom/9702018

On $δ_m$ constant locus of versal deformations of nondegenerate hypersurface simple K3 singularities

Masako Furuya
View original source ↗Read source document ↗Export metadata ↓

Abstract

Hypersurface simple K3 singularities defined by nondegenerate quasi-homogeneous polynomials are classified into ninety five classes in term of the weight of the polynomial by T. Yonemura. We consider versal deformations of them. It has been conjectured that the stratum $μ$ =const of the versal deformation of any nondegenerate hypersurface simple K3 singularity is equivalent to the $δ_m$ constant locus. It holds true for the case deformations are also nondegenerate by K. Watanabe. On the other hand, it follows from Reid that the $δ_m$ constant locus includes the $μ$ constant locus generally. We show the conjecture holds true in general for No.10-14, 46-51 and 83 in the table of Yonemura.

Explore related subjects

alg-geommath.AG

Keep this discovery

Explore connections, maps & timelines

BibTeXRIS

Masako Furuya. 1997-02-27. On $δ_m$ constant locus of versal deformations of nondegenerate hypersurface simple K3 singularities. https://arxiv.org/abs/alg-geom/9702018

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2019

Classification of Varieties with Canonical Curve Section via Gaussian maps on Canonical Curves

Let $C \subset P^{g-1}$ be a smooth canonical curve of genus $g \geq 3$. The purpose of this article is to further develop a method to classify varieties having $C$ as their curve section, using Gaussian map computations. In a previous article a careful analysis of the degeneration to the cone over the hyperplane section was made for _prime_ Fano threefolds, that is Fano threefolds whose Picard group is generated by the hyperplane bundle. In this article we extend this method and classify Fano threefolds of higher index (which still have Picard number one). We are also able to classify Mukai varieties, i.e. varieties of dimension four or more with canonical curve sections.

alg-geom↗
arXiv2017

Boundedness and $K^2$ for log surfaces

Let $ε, C$ be two positive real numbers, and $\mathcal C \subset \mathbb R$ be a DCC (descending chain condition) set. Let $(X, B = \sum b_j B_j)$ denote a projective surface with an $\mathbb R$-divisor. Then (1) The class $\{X\}$ of surfaces for which there exists a divisor $B$ such that $(X,B)$ is $ε$-log terminal and $-(K_X + B)$ is nef (excluding only those for which at the same time $K_X\equiv 0$, $B=0$, and $X$ has at worst Du Val singularities), is bounded. (2) The set $\{(K_X + B)^2\}$ of squares for the semi log canonical pairs $(X, B)$ with ample $K_X + B$ and $b_j \in \mathcal C$, is a DCC set. (3) The class $\{(X,B)\}$ of pairs such that $(X, B)$ is semi log canonical, $K_X + B$ is ample, $(K_X + B)^2 = C$ and $b_j \in \mathcal C$, is bounded.

alg-geom↗