相关论文: A cusp singularity with no Galois cover by a compl…

Using pagoda flop transitions between smooth projective threefolds, a relation is derived between the Euler numbers of moduli spaces of stable pairs which are scheme-theoretically supported on a fixed singular space curve and Euler numbers…

In this paper we study a special case of the completion of cusp K\"{a}hler-Einstein metric on the regular part of varieties by taking the continuity method proposed by La Nave and Tian. The differential geometric and algebro-geometric…

Thurston's Ending Lamination Conjecture states that a hyperbolic 3-manifold N with finitely generated fundamental group is uniquely determined by its topological type and its end invariants. In this paper we prove this conjecture for…

We classify simply-connected, complete Willmore surfaces with vanishing Gaussian curvature. We also study the Willmore cones and give a classification. As an application, we give a Bernstein-type theorem.

We consider smooth plane curves $\mathcal{X}$ of degree $d\geq4$, defined over an algebraically closed field of characteristic $0$, that possess a unique outer Galois point. This geometric condition forces the curve to be a cyclic covering…

Coalgebra-Galois extensions generalise Hopf-Galois extensions, which can be viewed as non-commutative torsors. In this paper it is analysed when a coalgebra-Galois extension is a separable, split, or strongly separable extension.

In this article, we will define non-commutative covering spaces using Hopf-Galois theory. We will look at basic properties of covering spaces that still hold for these non-commutative analogues. We will describe examples including coverings…

We study a natural generalization of transversally intersecting smooth hypersurfaces in a complex manifold: hypersurfaces, whose components intersect in a transversal way but may be themselves singular. Such hypersurfaces will be called…

The first and last named authors have demonstrated the existence of knots for which every integral slope is non-characterizing. In this short note, we extend this result in two ways. There exists a knot that shares for every integer n the…

The empty set of course contains no computable point. On the other hand, surprising results due to Zaslavskii, Tseitin, Kreisel, and Lacombe assert the existence of NON-empty co-r.e. closed sets devoid of computable points: sets which are…

We study the equation for improper (parabolic) affine spheres from the view point of contact geometry and provide the generic classification of singularities appearing in geometric solutions to the equation as well as their duals. We also…

We discuss an example related to the method of Brody. The example is an open subset of a compact complex torus which is covered by entire curves, but not by Brody curves.

In this paper we classify the unimodal isolated complete intersection singularities in arbitrary characteristic under contact equivalence. The classification over $\mathbb{C}$ has already done by A. Dimca and C.G. Gibson. We continue and…

We obtain a criterion for an analytic subset of a Euclidean space to contain points of differentiability of a typical Lipschitz function, namely, that it cannot be covered by countably many sets, each of which is closed and purely…

We describe an algorithm that determines a set of unramified covers of a given hyperelliptic curve, with the property that any rational point will lift to one of the covers. In particular, if the algorithm returns an empty set, then the…

We analyse the breaking of conformal invariance for null polygonal Wilson loops in ${\cal N}=4$ SYM beyond that induced by the UV divergences due to the cusps. It only shows up in exceptional configurations, where the polygon intersects the…

We prove new lower bounds on the crossing number of a complete graphs assuming that it is drawn in such a way that it contains a Hamiltonian cycle with no crossings.

We prove that there exists an integer p_0 such that X_split(p)(Q) is made of cusps and CM-points for any prime p>p_0. Equivalently, for any non-CM elliptic curve E over Q and any prime p>p_0 the image of the Galois representation induced by…

The cuspidalization conjecture, which is a consequence of Grothendieck's section conjecture, asserts that for any smooth hyperbolic curve $X$ over a finitely generated field $k$ of characteristic $0$ and any non empty Zariski open $U…

In a recent work, authors prove a yet another no-go theorem that forbids the existence of a universal probabilistic quantum protocol producing a superposition of two unknown quantum states. In this short note, we show that in the presence…