相关论文: Computational Geometry Column 32

We formulate a relative analogue of the Clemens conjectures for 1/2-log Calabi-Yau threefold pairs (X,Y) (where K_X+2Y is isomorphic to O_X). This framework rests on the restoration of a perfect deformation/obstruction duality specific to…

Reay's relaxed Tverberg conjecture and Conway's thrackle conjecture are open problems about the geometry of pairwise intersections. Reay asked for the minimum number of points in Euclidean d-space that guarantees any such point set admits a…

We show that there are at most finitely many one cusped orientable hyperbolic 3-manifolds which have more than eight non-hyperbolic Dehn fillings. Moreover, we show that determining these finitely many manifolds is decidable.

We prove that for any distance at least 3 Heegaard splitting and a boundary component $F$, there is a diameter finite ball in the curve complex $\mathcal {C}(F)$ so that it contains all distance degenerate curves or slopes in $F$.

We prove that double exponentiation is an upper bound to Ramsey theorem for colouring of pairs when we want to predetermine the order of the differences of successive members of the homogeneous set.

We prove that the Riemannian geometry of almost K\"ahler manifolds can be expressed in terms of the Poisson algebra of smooth functions on the manifold. Subsequently, K\"ahler-Poisson algebras are introduced, and it is shown that a…

We introduce Koszul modules associated with (graded) Kac-Moody Lie algebras. We provide a precise criterion for when these modules are of finite length. As an exemplary application we deduce a bound on the dimension of the second graded…

We obtain new upper and lower bounds on the number of unit perimeter triangles spanned by points in the plane. We also establish improved bounds in the special case where the point set is a section of the integer grid.

We consider plane curves isomorphic to C*. We prove that with one exception the branches at infinity can be separated by an automorphism of C^2. We also give a bound for selfintersection number of the resolution curve.

We show upper and lower bounds for angles in iterations of trisections of certain triangulations.

In this short note, we provide a new infinite family of $K_{2, t+1}$-free graphs for each prime power $t$. Using these graphs, we show that it is possible to partition the edges of $K_n$ into parts, such that each part is isomorphic to our…

Motivated by the study of collapsing Calabi-Yau threefolds with a Lefschetz K3 fibration, we construct a complete Calabi-Yau metric on $\mathbb{C}^3$ with maximal volume growth, which in the appropriate scale is expected to model the…

We prove that the boundary of the future of a surface $K$ consists precisely of the points $p$ that lie on a null geodesic orthogonal to $K$ such that between $K$ and $p$ there are no points conjugate to $K$ nor intersections with another…

We give a short, topological proof that all graphs admit tree-decompositions displaying their topological ends.

We give two new conditions on topological $k$-graphs that are equivalent to the Yeend's aperiodicity Condition (A). Each of the new conditions concerns finite paths rather than infinite. We use a specific example, resulting from a new…

We prove a new fractional Helly theorem for families of sets obeying topological conditions. More precisely, we show that the nerve of a finite family of open sets (and of subcomplexes of cell complexes) in R^d is k-Leray where k depends on…

We give a new bound for the large sieve inequality with power moduli q^k that is uniform in k. The proof uses a new theorem due to T. Wooley from his work on efficient congruencing.

We explain how the current knowledge on the set of complete noncompact constant mean curvature surfaces can be exploited to produce new examples of compact constant mean curvature surfaces of genus greater than or equal to 3.

We provide a simple proof of a computable analogue to the Jayne Rogers Theorem from descriptive set theory. The difficulty of the proof is delegated to a simulation result pertaining to non-deterministic type-2 machines. Thus, we…

David Gabai showed that disk decomposable knot and link complements carry taut foliations of depth one. In an arbitrary sutured 3-manifold M, such foliations F, if they exist at all, are determined up to isotopy by an associated ray [F]…