Projective resolutions of topological spaces

Virtual Resolutions for a Product of Projective Spaces

Syzygies capture intricate geometric properties of a subvariety in projective space. However, when the ambient space is a product of projective spaces or a more general smooth projective toric variety, minimal free resolutions over the Cox ring are too long and contain many geometrically superfluous summands. In this paper, we construct some much shorter free complexes that better encode the ge...

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.

Crepant Resolutions of Weighted Projective Spaces and Quantum Deformations

We compare the Chen-Ruan cohomology ring of the weighted projective spaces P(1, 3, 4, 4) and P(1, ..., 1, n) with the cohomology ring of their crepant resolutions. In both cases, we prove that the Chen-Ruan cohomology ring is isomorphic to the quantum corrected cohomology ring of the crepant resolution after suitable evaluation of the quantum parameters. For this, we prove a formula for the Gro...

Topological K-theory of Complex Projective Spaces

We compute the K-theory of complex projective spaces. There are three major ingredients: the exact sequence of K-groups, the theory of Chern character and the Bott Periodicity Theorem.

Projective limits of topological vector spaces