Topological Triviality of $μ$-constant Deformations of Type f(x) + tg(x)

Adam Parusinski

Home/Archive/arXiv

arXiv · alg-geom/9711014

Topological Triviality of $μ$-constant Deformations of Type f(x) + tg(x)

Adam Parusinski

View original source ↗Read source document ↗Export metadata ↓

Abstract

We show that every $μ$-constant family of isolated hypersurface singularities of type f(x) + tg(x), where t is a parameter, is topologically trivial. In the proof we construct explicitely a vector field trivializing the family. The proof uses only the curve selection lemma and hence, for an appropriately translated statement, also works over the reals. Some applications to the study of singularities at infinity of complex polynomials are given.

Explore related subjects

alg-geom math.AG

Keep this discovery

Explore connections, maps & timelines

BibTeX RIS

Adam Parusinski. 1997-11-11. Topological Triviality of $μ$-constant Deformations of Type f(x) + tg(x). https://arxiv.org/abs/alg-geom/9711014

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

KEEP EXPLORING

Related papers

arXiv2025

Deforming Calabi-Yau Threefolds

This paper first generalises the Bogomolov-Tian-Todorov unobstructedness theorem to the case of Calabi-Yau threefolds with canonical singularities. The deformation space of such a Calabi-Yau threefold is no longer smooth, but the general principle is that the obstructions to deforming such a threefold are precisely the obstructions to deforming the singularities of the threefold. Secondly, these results are applied to smoothing singular Calabi-Yau threefolds with crepant resolutions. Any such Calabi-Yau threefold with isolated complete intersection singularities which are not ordinary double points is smoothable. A Calabi-Yau threefold with non-complete intersection isolated singularities is proved to be smoothable under much stronger hypotheses.

alg-geom↗

arXiv2025

Derived categories of coherent sheaves on abelian varieties and equivalences between them

We study derived categories of coherent sheaves on abelian varieties. We give a criterion for the equivalence of the derived categories on two abelian varieties. We describe the autoequivalence group for the derived category of coherent sheaves of an abelian variety.

alg-geom↗

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↗