The projective dimension of valuated vector spaces

Quantum Dimension and Quantum Projective Spaces

We show that the family of spectral triples for quantum projective spaces introduced by D’Andrea and Da̧browski, which have spectral dimension equal to zero, can be reconsidered as modular spectral triples by taking into account the action of the element K2ρ or its inverse. The spectral dimension computed in this sense coincides with the dimension of the classical projective spaces. The connecti...

Projective limits of topological vector spaces

Stable Geometric Dimension of Vector Bundles over Odd-dimensional Real Projective Spaces

In [6], the geometric dimension of all stable vector bundles over real projective space P was determined if n is even and sufficiently large with respect to the order 2 of the bundle in K̃O(P). Here we perform a similar determination when n is odd and e > 6. The work is more delicate since P does not admit a v1-map when n is odd. There are a few extreme cases which we are unable to settle precis...

Stable Geometric Dimension of Vector Bundles over Even-dimensional Real Projective Spaces

In 1981, Davis, Gitler, and Mahowald determined the geometric dimension of stable vector bundles of order 2e over RPn if n is even and sufficiently large and e ≥ 75. In this paper, we use the Bendersky-Davis computation of v−1 1 π∗(SO(m)) to show that the 1981 result extends to all e ≥ 5 (still provided that n is sufficiently large). If e ≤ 4, the result is often different due to anomalies in t...

Resolutions of Segre embeddings of projective spaces of any dimension

This paper deals with syzygies of the ideals of the Segre embeddings. Let d ≥ 3 and n1, ..., nd ∈ N − {0}. We prove that OPn1×....×Pnd (1, ..., 1) satisfies Green-Lazarsfeld’s Property Np if and only if p ≤ 3.