We consider Voronoi diagrams deened on the oriented projective plane T 2. In this geometry, the closest and furthest site diagrams are antipodal. We give a simple on-line incremental algorithm for constructing the additively weighted diagram. This diagram, which may be disconnected in Euclidean plane, is always connected in T 2 and has exactly 3n ? 6 edges and 2n ? 4 vertices, where n is the nu...

Motivated by previous work on deformation theory of higher order theta-characteristics, we introduce a weighted Gaussian map γa,b(X,L), where a, b are positive integers, X is a smooth projective variety, L is a line bundle on X and γ1,1(X,L) is the ordinary Gaussian map for (X,L). We establish a sharp lower bound on its rank and we investigate the extremal cases for curves. MSC 2000: 14H99, 14F10

We investigate the existence and non-existence of maximal green sequences for quivers arising from weighted projective lines. Let Q be Gabriel quiver endomorphism algebra a basic cluster-tilting object in cluster category \(\mathcal {C}_{\mathbb {X}}\) line \(\mathbb {X}\). It is proved that there exists \(Q^{\prime }\) mutation equivalence class Mut(Q) such admits sequence. Furthermore, which ...

Starting from the quantum differential equation associated to a weighted projective space, which is given by Coates, Corti, Lee and Tseng, we construct a Frobenius manifold. We see that the Frobenius manifold coincides with the big quantum cohomology of the weighted projective space. The construction is based on Dubrovin’s reconstruction theorem.

We study the gonality and the existence of low degree pencils on curves with a model on a weighted projective plane, when their singularities are only ordinary nodes or ordinary cusps and they are general in the weighted projective plane. M.S.C. 2010: 14H51, 14J26.

We study the topological K-theory spectrum of the dg singularity category associated to a weighted projective complete intersection. We calculate the topological K-theory of the dg singularity category of a weighted projective hypersurface in terms of its Milnor fiber and monodromy operator, and, as an application, we obtain a lift of the Atiyah-Bott-Shapiro construction to the level of spectra.

We consider the question of determining the maximum number of Fqrational points that can lie on a hypersurface of a given degree in a weighted projective space over the finite field Fq, or in other words, the maximum number of zeros that a weighted homogeneous polynomial of a given degree can have in the corresponding weighted projective space over Fq. In the case of classical projective spaces...