Related papers: The Bruce-Roberts Numbers of 1-Forms on an ICIS

This work investigates invariants, including the GSV-index, the local Euler obstruction, and the Brasselet number, within the context of isolated complete intersection singularities (ICIS). The goal is to forge connections among these…

We introduce the notion of the \textit{Bruce-Roberts number} for holomorphic 1-forms relative to complex analytic varieties. Our main result shows that the Bruce-Roberts number of a 1-form $\omega$ with respect to a complex analytic…

We introduce the notion of the Bruce-Roberts Tjurina number for holomorphic 1-forms relative to a pair $(X,V)$ of complex analytic subvarieties. When the pair $(X,V)$ consists of isolated complex analytic hypersurfaces, we prove that the…

We give formulas for the Bruce-Roberts number $\mu_{BR}(f,X)$ and its relative version $\mu_{BR}^{-}(f,X)$ of a function $f$ with respect to an ICIS $(X,0)$. We show that $\mu_{BR}^{-}(f,X)=\mu(f^{-1}(0)\cap X,0)+\mu(X,0)-\tau(X,0)$, where…

We study deformations of holomorphic function germs $f:(X,0)\to\mathbb C$ where $(X,0)$ is an ICIS. We present conditions for these deformations to have constant Milnor number, Euler obstruction and Bruce-Roberts number.

We collect some classical results about holomorphic 1-forms of a reduced complex curve singularity, in particular of a complete intersection, and use them to compare the Milnor number, the Tjurina number and the dimension of the torsion…

Equivariant versions of the radial index and of the GSV-index of a vector field or a 1-form on a singular variety with an action of a finite group are defined. They have values in the Burnside ring of the group. Poincar\'e-Hopf type…

If two G-manifolds are G-cobordant then characteristic numbers corresponding to the fixed point sets (submanifolds) of subgroups of G and to normal bundles to these sets coincide. We construct two analogues of these characteristic numbers…

Let $(X,0)$ be the germ of an equidimensional analytic set in $(\mathbb C^n,0)$ and $f=(f_1,f_2)$ a map-germ into the plane defined on $X.$ In this work, we investigate topological invariants associated to the pair $(f,X),$ among them, the…

We discuss different generalizations of the classical notion of the index of a singular point of a vector field to the case of vector fields or 1-forms on singular varieties, describe relations between them and formulae for their…

We consider 1-forms on, so called, essentially isolated determinantal singularities (a natural generalization of isolated ones), show how to define analogues of the Poincar\'e--Hopf index for them, and describe relations between these…

We collect some classical results about holomorphic 1-forms of a reduced complex curve singularity. They are used to study the pull-back of holomorphic 1-forms on an isolated complete intersection curve singularity under the normalization…

We introduce a notion of a homological index of a holomorphic 1-form on a germ of a complex analytic variety with an isolated singularity, inspired by X. G\'omez-Mont and G.-M. Greuel. For isolated complete intersection singularities it…

There are some generalizations of the classical Eisenbud-Levine-Khimshashvili formula for the index of a singular point of an analytic vector field on $R^n$ for vector fields on singular varieties. We offer an alternative approach based on…

For a G-invariant holomorphic 1-form with an isolated singular point on a germ of a complex-analytic G-variety with an isolated singular point (G is a finite group) one has notions of the equivariant homological index and of the (reduced)…

We compute the spectrum and Smith normal form of the incidence matrix of disjoint transversals, a combinatorial object closely related to the n-dimensional case of Rota's basis conjecture.

This is a concise overview of the definitions and properties of the linking number and its higher-order generalization, Milnor invariants.

The isotropy of multiples of Pfister forms is studied. In particular, an improved lower bound on the value of their first Witt index is obtained. This result and certain of its corollaries are applied to the study of the weak isotropy index…

We consider infinitely convolved Bernoulli measures (or simply Bernoulli convolutions) related to the $\beta$-numeration. A matrix decomposition of these measures is obtained in the case when $\beta$ is a PV number. We also determine their…

This article is about 1-forms on complex analytic varieties and it is particularly relevant when the variety has non-isolated singularities. We first show how the radial extension technique of M.-H. Schwartz can be adapted to 1-forms,…