In this article, we study shape fitting problems, -coresets, and total sensitivity. We focus on the (j, k)-projective clustering problems, including k-median/k-means, k-line clustering, j-subspace approximation, and the integer (j, k)-projective clustering problem. We derive upper bounds of total sensitivities for these problems, and obtain -coresets using these upper bounds. Using a dimension-...

0. Introduction i. Weighted projective space i.i. Notations 1.2. Interpretations 1.3. The first properties 1.4. Cohomology of 0F(n) 1.5. Pathologies 2. Bott's theorem 2.1. The sheaves ~(n) 2.2. Justifications 2.3. Cohomology of ~$(n) 3. Weighted complete intersections 3.1. Quasicones 3.2. Complete intersections 3.3. The dualizing sheaf 3.4. The Poincare series 3.5. Examples 4. The Hodge structu...

We study the inverse spectral problem for weighted projective spaces using wave-trace methods. We show that in many cases one can “hear” the weights of a weighted projective space.

We study the inverse spectral problem for weighted projective spaces using wave-trace methods. We show that in many cases one can “hear” the weights of a weighted projective space.

Chen and Ruan [6] defined a very interesting cohomology theory-Chen-Ruan orbifold cohomology. The primary objective of this paper is to compute the Chen-Ruan orbifold cohomology of weighted projective space, one of the most important space used in physics. The classical tools (orbifold cohomology defined by Chen and Ruan,toric varieties, the localization formula) which have been proved to be su...

Chen and Ruan [6] defined a very interesting cohomology theoryChen-Ruan orbifold cohomology. The primary objective of this paper is to compute the Chen-Ruan orbifold cohomology of weighted projective space, one of the most important space used in physics. The classical tools (orbifold cohomology defined by Chen and Ruan,toric varieties, the localization formula) which have been proved to be suc...

The algebraic approach to bundles in non-commutative geometry and the definition of quantum real weighted projective spaces are reviewed. Principal U(1)-bundles over quantum real weighted projective spaces are constructed. As the spaces in question fall into two separate classes, the negative or odd class that generalises quantum real projective planes and the positive or even class that genera...

We calculate the small quantum orbifold cohomology of arbitrary weighted projective spaces. We generalize Givental’s heuristic argument, which relates small quantum cohomology to S-equivariant Floer cohomology of loop space, to weighted projective spaces and use this to conjecture an explicit formula for the small J-function, a generating function for certain genuszero Gromov–Witten invariants....