Related papers: Monodromy of Hypersurface Singularities
In this paper, we propose new algorithms for finding a common point of the solution set of a pseudomonotone equilibrium problem and the set of fixed points of a symmetric generalized hybrid mapping in a real Hilbert space. The convergence…
Classifications of all biharmonic isoparametric hypersurfaces in the unit sphere, and all biharmonic homogeneous real hypersurfaces in the complex or quaternionic projective spaces are shown. Answers in case of bounded geometry to Chen's…
We study the uniqueness of horospheres and equidistant spheres in hyperbolic space under different conditions. First we generalize the Bernstein theorem by Do Carmo and Lawson to the embedded hypersurfaces with constant higher order mean…
We describe, study, and experiment with an algorithm for finding all solutions of systems of polynomial equations using homotopy continuation and monodromy. This algorithm follows a framework developed in previous work and can operate in…
I describe the monodromy of smooth hypersurfaces $X$ of high degree in a fixed smooth variety $Y$ containing a fixed subvariety $W$ of $Y$. The cohomology of $X$ in middle degree spanned by the pull-back of the cohomology of $Y$ and by the…
The geometric monodromy of a plane curve singularity is a quasi-finite diffeomorphism. In this paper we locate the reduction curves of the geometric monodromy and the quadratic vanishing cycles of the singularity. An application to the…
In this paper, we develop a multiscale method for solving the Signorini problem with a heterogeneous field. The Signorini problem is encountered in many applications, such as hydrostatics, thermics, and solid mechanics. It is well-known…
Conventional ways to solve optimization problems on low-rank matrix sets which appear in great number of applications ignore its underlying structure of an algebraic variety and existence of singular points. This leads to appearance of…
Isolated hypersurface singularities come equipped with a Milnor lattice, a ${\mathbb Z}$-lattice of finite rank, and a set of $distinguished$ ${\mathbb Z}$-bases of this lattice. Usually these bases are constructed from $one$ morsification…
We study immersed surfaces in smooth 4-manifolds via singular banded unlink diagrams. Such a diagram consists of a singular link with bands inside a Kirby diagram of the ambient 4-manifold, representing a level set of the surface with…
This paper continues our researches \cite{DS1, DS2, DS3} by computing some invariants based on Hilbert-Poincar\'{e} series associated to Milnor algebras. Our computations are for some of the classical surfaces and 3-folds with different…
We introduce spectral Hirzebruch-Milnor classes for singular hypersurfaces. These can be identified with Steenbrink spectra in the isolated singularity case, and may be viewed as their global analogues in general. Their definition uses…
We introduce a combinatorial argument to study closed minimal hypersurfaces of bounded area and high Morse index. Let $(M^{n+1},g)$ be a closed Riemannian manifold and $\Sigma\subset M$ be a closed embedded minimal hypersurface with area at…
Recently holographic prescriptions are proposed to compute quantum complexity of a given state in the boundary theory. A specific proposal known as `holographic subregion complexity' is supposed to calculate the the complexity of a reduced…
We use stratified Morse theory to construct a complex to compute the cohomology of the complement of a hyperplane arrangement with coefficients in a complex rank one local system. The linearization of this complex is shown to be the…
We adapt algorithms for resolving the singularities of complex algebraic varieties to prove that the natural map of homology theories from complex bordism to the bordism theory of complex derived orbifolds splits. In equivariant stable…
In this paper, we first classify singular fibers of proper $C^\infty$ stable maps of 3-dimensional manifolds with boundary into surfaces. Then, we compute the cohomology groups of the associated universal complex of singular fibers, and…
The method of monodromy is an important tool for computing Virasoro conformal blocks in a two-dimensional Conformal Field Theory (2d CFT) at large central charge and external dimensions. In deriving the form of the monodromy problem, which…
We construct a formal connection on the Aomoto complex of an arrangement of hyperplanes, and use it to study the Gauss-Manin connection for the moduli space of the arrangement in the cohomology of a complex rank one local system. We prove…
We develop a new symbolic-numeric algorithm for the certification of singular isolated points, using their associated local ring structure and certified numerical computations. An improvement of an existing method to compute inverse systems…