Related papers: A tessellation for algebraic surfaces in CP3
We study the fixed singularities imposed on members of a linear system of surfaces in P^3_C by its base locus Z. For a 1-dimensional subscheme Z \subset P^3 with finitely many points p_i of embedding dimension three and d >> 0, we determine…
A complete method is proposed to compute a certified, or ambient isotopic, meshing for an implicit algebraic surface with singularities. By certified, we mean a meshing with correct topology and any given geometric precision. We propose a…
A 2-cell embedding of a graph $G$ into a closed (orientable or nonorientable) surface is called regular if its automorphism group acts regularly on the flags - mutually incident vertex-edge-face triples. In this paper, we classify the…
We study and classify regular and semi-regular tessellations of Riemann surfaces of various genera and investigate their corresponding supersymmetric gauge theories. These tessellations are generalizations of brane tilings, or bipartite…
To any graded Frobenius algebra A we associate a sequence of graded Frobenius algebras A^[n] in such a way that for any smooth projective surface X with trivial canonical divisor there is a canonical isomorphism of rings between (H*X)^[n]…
We introduce the notion of fundamental heap for compact orientable surfaces with boundary embedded in $3$-space, which is an isotopy invariant of the embedding. It is a group, endowed with a ternary heap operation, defined using diagrams of…
A Kauffman bracket on a surface is an invariant for framed links in the thickened surface, satisfying the Kauffman skein relation and multiplicative under superposition. This includes representations of the skein algebra of the surface. We…
We show that a Hilbert scheme of conics on a Fano fourfold double cover of $\mathbb{P}^2\times\mathbb{P}^2$ ramified along a divisor of bidegree $(2,2)$ admits a $\mathbb{P}^1$-fibration with base being a hyper-K\"{a}hler fourfold. We…
The problem of uniformly placing N points onto a sphere finds applications in many areas. For example, points on the sphere correspond to unit quaternions as well as to the group of rotations SO(3) and the online version of generating…
Computing the topology of an algebraic plane curve $\mathcal{C}$ means to compute a combinatorial graph that is isotopic to $\mathcal{C}$ and thus represents its topology in $\mathbb{R}^2$. We prove that, for a polynomial of degree $n$ with…
Complex tetrahedral surface $\mathcal{T}$ is a non planar projective surface that is generated by four intersecting complex projective planes $CP^{2}$. In this paper, we study the family $\{\mathcal{T}_{m}\} $ of blow ups of $\mathcal{T}$…
Let $K$ be a $k$-dimensional simplicial complex having $n$ faces of dimension $k$, and $M$ a closed $(k-1)$-connected PL $2k$-dimensional manifold. We prove that for $k\ge3$ odd $K$ embeds into $M$ if and only if there are $\bullet$ a…
W. Thurston proved that to a triangulation of the sphere of non-negative combinatorial curvature, one can associate an element in a certain lattice over the Eisenstein integers such that its orbit is a complete invariant of the…
Three dimensional topological superconductors (TScs) protected by time reversal (T) symmetry are characterized by gapless Majorana cones on their surface. Free fermion phases with this symmetry (class DIII) are indexed by an integer n, of…
We consider threefolds that admit a fibration by K3 surfaces over a nonsingular curve, equipped with a divisorial sheaf that defines a polarisation of degree two on the general fibre. Under certain assumptions on the threefold we show that…
This paper introduces a novel method for the efficient and accurate computation of volume fractions on unstructured polyhedral meshes, where the phase boundary is an orientable hypersurface, implicitly given as the iso-contour of a…
We study invariants coming from certain optimisation problems for nef divisors on surfaces. These optimisation problems arise in work of the author and collaborators tying obstructions to embeddings between symplectic 4-manifolds to…
Let F be a closed non-orientable surface. We classify all finite order invariants of immersions of F into R^3, with values in any Abelian group. We show they are all functions of the universal order 1 invariant that we construct as T \oplus…
Up to isomorphism there are six fixed-point free crystallographic groups in Euclidean Space generated by twists (screw motions). In each case, an orientable 3-manifold is obtained as the quotient of E3 by such a group. The cubic…
An irregular vertex in a tiling by polygons is a vertex of one tile and belongs to the interior of an edge of another tile. In this paper we show that for any integer $k\geq 3$, there exists a normal tiling of the Euclidean plane by convex…