Related papers: Normal forms for rational 3-tangles

In this article we classify normal forms and unfoldings of linear maps in eigenspaces of (anti)-automorphisms of order two. Our main motivation is provided by applications to linear systems of ordinary differential equations, general and…

Suppose $K$ is an unknot lying in the 1-skeleton of a triangulated 3-manifold with $t$ tetrahedra. Hass and Lagarias showed there is an upper bound, depending only on $t$, for the minimal number of elementary moves to untangle $K$. We give…

Any smooth projective curve embeds into $\mathbb{P}^3$. More generally, any curve embeds into a rationally connected variety of dimension at least three. We prove conversely that if every curve embeds in a threefold $X$, then $X$ is…

We consider a rational-trigonometric deformation in context of rational and trigonometric deformations. The simplest examples of these deformations are presented in different fields of mathematics. Rational-trigonometric differential…

The normal form for a system of ode's is constructed from its polynomial symmetries of the linear part of the system, which is assumed to be semi-simple. The symmetries are shown to have a simple structure such as invariant function times…

This paper initiates the study of a class of schemes that we call correspondence scrolls, which includes the rational normal scrolls and linearly embedded projective bundle of decomposable bundles, as well as degenerate K3 surfaces,…

We exploit the equivalence between $t$-structures and normal torsion theories on a stable $\infty$-category to show how a few classical topics in the theory of triangulated categories, i.e., the characterization of bounded $t$-structures in…

We show that a standard conic bundle over a minimal rational surface is rational and its Jacobian splits as the direct sum of Jacobians of curves if and only if its derived category admits a semiorthogonal decomposition by exceptional…

Most algorithms constructing bases of finite-dimensional vector spaces return basis vectors which, apart from orthogonality, do not show any special properties. While every basis is sufficient to define the vector space, not all bases are…

A permutation graph is a graph that can be derived from a permutation, where the vertices correspond to letters of the permutation, and the edges represent inversions. We provide a construction to show that there are infinitely many…

We prove that the orbit closure of the determinant is not normal. A similar result is obtained for the orbit closure of the permanent multiplied by a power of a linear form.

We establish normal form theorems for a large class of singular flat connections on complex manifolds, including connections with logarithmic poles along weighted homogeneous Saito free divisors. As a result, we show that the moduli spaces…

We consider the motion by curvature of a network of smooth curves with multiple junctions in the plane, that is, the geometric gradient flow associated to the length functional. Such a flow represents the evolution of a two--dimensional…

For every algebraically closed field $\boldsymbol k$ of characteristic different from $2$, we prove the following: (1) Generic finite dimensional (not necessarily associative) $\boldsymbol k$-algebras of a fixed dimension, considered up to…

We develop a Hodge theory for relative simple normal crossing varieties over an Artinian base scheme. We introduce the notion of a mixed Hodge structure over an Artin ring, which axiomatizes the structure that is found on the cohomology of…

We describe a procedure for constructing formal normal forms of holomorphic maps with a hypersurface of fixed points, and we apply it to obtain a complete list of formal normal forms for 2-dimensional holomorphic maps tangential to a curve…

The family of Euclidean triangles having some fixed perimeter and area can be identified with a subset of points on a nonsingular cubic plane curve, i.e., an elliptic curve; furthermore, if the perimeter and the square of the area are…

In this paper, we define the rectangle condition on the bridge sphere for a $n$-bridge decomposition of a knot whose definition is analogous to the definition of the rectangle condition for Heegaard splittings of $3$-manifolds. We show that…

We introduce a notion of cross-flips: local moves that transform a balanced (i.e., properly $(d+1)$-colored) triangulation of a combinatorial $d$-manifold into another balanced triangulation. These moves form a natural analog of bistellar…

Partial connections are (singular) differential systems generalizing classical connections on principal bundles, yielding analogous decompositions for manifolds with nonfree group actions. Connection forms are interpreted as maps…