a projective parameter of a geodesic as solution of certain ode is defined to be a parameter which is invariant under projective change of metric. using projective parameter and poincaré metric, an intrinsic projectively invariant pseudo-distance can be constructed. in the present work, solutions of the above ode are characterized with respect to the sign of parallel ricci tensor on a finsler s...

2 Vector Spaces and Projective Spaces 3 2.1 Vector spaces and their duals . . . . . . . . . . . . . . . . . . . . . . . . . 3 2.2 Projective spaces and homogeneous coordinates . . . . . . . . . . . . . . . 5 2.2.1 Visualizing projective space . . . . . . . . . . . . . . . . . . . . . . 5 2.2.2 Homogeneous coordinates . . . . . . . . . . . . . . . . . . . . . . . 6 2.3 Linear subspaces . . . . ....

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In this paper, embeddings φ : M → P from a linear space (M,M) in a projective space (P,L) are studied. We give examples for dimM > dimP and show under which conditions equality holds. More precisely, we introduce properties (G) (for a line L ∈ L and for a plane E ⊂ M it holds that |L ∩ φ(M)| 6 = 1) and (E) (φ(E) = φ(E) ∩ φ(M), whereby φ(E) denotes the by φ(E) generated subspace of P ). If (G) a...

We characterise mutations between fake weighted projective spaces, and give explicit formulas for how the weights and multiplicity change under mutation. In particular, we prove that multiplicity-preserving mutations between fake weighted projective spaces are mutations over edges of the corresponding simplices. As an application, we analyse the canonical and terminal fake weighted projective s...

We investigate the Cohomological Crepant Resolution Conjecture for reduced Gorenstein weighted projective spaces. Using toric methods, we prove this conjecture in some new cases. As an intermediate step, we show that weighted projective spaces are toric Deligne-Mumford stacks. We also describe a combinatorial model for the orbifold cohomology of weighted projective spaces.