Related papers: On the Structure of Second Jacobian Ideals

We study the holomorphic equivalence problem for finite type hypersurfaces in $\mathbb C^2$. We discover a geometric condition, which is sufficient for the existence of a natural convergent normal form for a finite type hypersurface. We…

Given a Delaunay decomposition of a compact hyperbolic surface, one may record the topological data of the decomposition, together with the intersection angles between the `empty disks' circumscribing the regions of the decomposition. The…

The decomposition into interaction subspaces is a hierarchical decomposition of the spaces of cylindrical functions of a finite product space, also called factor spaces. It is an important construction in graphical models and a standard way…

The paper contains a general construction which produces new examples of non simply-connected smooth projective surfaces. We analyze the resulting surfaces and their fundamental groups. Many of these fundamental groups are expected to be…

A quantum integrable model is considered which describes a quantization of affine hyper-elliptic Jacobian. This model is shown to possess the property of duality: a dual model with inverse Planck constant exists such that the…

The duality between coherent quantum phase slip and Josephson junction in nanosheets was investigated using the dual Hamiltonian method. This is equivalent to the duality between superconductivity and superinsulator in the 2 + 1 dimension…

The relativistic membrane equation can be rewritten as a first order hyperbolic system. Making use of the characteristic decomposition method, a new blow-up theorem is established. As an application, it demonstrates the formation of…

In this article, we prove that for a finite quiver $Q$ the equivalence class of a potential up to formal change of variables of the complete path algebra $\widehat{\mathbb{C} Q}$, is determined by its Jacobi algebra together with the class…

Primary decomposition of commutative monoid congruences is insensitive to certain features of primary decomposition in commutative rings. These features are captured by the more refined theory of mesoprimary decomposition of congruences,…

Based on the vanishing of the second Hochschild cohomology group of the enveloping algebra of the Heisenberg algebra it is shown that differential algebras coming from quantum groups do not provide a non-trivial deformation of quantum…

The holomorphy conjecture predicts that the local Igusa zeta function associated to a hypersurface and a character is holomorphic on $\mathbb{C}$ whenever the order of the character does not divide the order of any eigenvalue of the local…

We study the existence of a Chow-theoretic decomposition of the diagonal of a smooth cubic hypersurface, or equivalently, the universal triviality of its ${\rm CH}_0$-group. We prove that for odd dimensional cubic hypersurfaces or for cubic…

In this work we discuss stability and nondegeneracy properties of some special families of minimal hypersurfaces embedded in $\mathbb{R}^m\times \mathbb{R}^n$ with $m,n\geq 2$. These hypersurfaces are asymptotic at infinity to a fixed…

We compute Hochschild cohomology of projective hypersurfaces starting from the Gerstenhaber-Schack complex of the (restricted) structure sheaf. We are particularly interested in the second cohomology group and its relation with…

Commutative supersymmetric Yang-Mills is known to be renormalizable for ${\cal N} = 1, 2$, while finite for ${\cal N} = 4$. However, in the noncommutative version of the model (NCSQED$_4$) the UV/IR mechanism gives rise to infrared…

This article is part of an ongoing investigation of the two-dimensional Jacobian conjecture. In the first paper of this series, we proved the generalized Magnus' formula. In this paper, inspired by cluster algebras, we introduce a sequence…

We consider a pair (H,I) where I is an involutive ideal of a Poisson algebra and H lies in I. We show that if I defines a 2n-gon singularity then, under arithmetical conditions on H, any deformation of H can "integrated" as a deformation of…

We construct, for a second-order homogeneous Lagrangian in two independent variables, a differential 2-form with the property that it is closed precisely when the Lagrangian is null. This is similar to the property of the 'fundamental…

We study the geometry of homogeneous hypersurfaces and their focal sets in complex hyperbolic spaces. In particular, we provide a characterization of the focal set in terms of its second fundamental form and determine the principal…

By results of the author there exists a projective (holomorphic) symplectic desingularization of the moduli space of rank-two torsion-free sheaves on a genus-two Jacobian with $c_1=0$ and $c_2=2$. This desingularization has a natural map to…