Algebraic Intersection Spaces

Geske, Christian

doi:10.48550/arxiv.1802.03871

Cited by 1 publication

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“…where f and c are the canonical morphisms, a = τ ≤q(r) j r * j * r g and b = j r * j * r g. Moreover, a and c are isomorphisms and the composition λ = a −1 • c −1 • b is a retract of f . So, the triangle (11) is split by Lemma 7.1.…”

Section: 2mentioning

confidence: 99%

“…In a recent paper [11], Genske takes a new viewpoint: instead of only giving up the topological construction and focusing in producing a complex of sheaves at the original space, he constructs a complex of vector spaces which is related with the complex computing the (co)homology of the original space X, but that satisfies Poincaŕe duality. The construction is valid for any analytic variety (Poincaré duality is satisfied in the compact case).…”

Section: Introductionmentioning

confidence: 99%

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Intersection Space Constructible Complexes

Agustin¹,

Bobadilla²

2018

Preprint

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We present an obstruction theoretic inductive construction of intersection space pairs, which generalizes Banagl's construction of intersection spaces for arbitraty depth stratifications. We construct intersection space pairs for pseudomanifolds with compatible trivial structures at the link fibrations; this includes the case of toric varieties. We define intersection space complexes in an axiomatic way, similar to Goresky-McPherson axioms for intersection cohomology. We prove that if the intersection space exists, then the pseudomanifold has an intersection space complex whose hypercohomology recovers the cohomology of the intersection space pair. We characterize existence and uniqueness of intersection space complexes in terms of the derived category of constructible complexes. We show that intersection space complexes of algebraic varieties lift to the derived category of Mixed Hodge Modules, endowing intersection space cohomology with a Mixed Hodge Structure. We find classes of examples admitting intersection space complex, and counterexamples not admitting them; they are in particular the first examples known not admitting Banagl intersection spaces. We prove that the (shifted) Verdier dual of an intersection space complex is an intersection space complex. We prove a generic Poincare duality theorem for intersection space complexes.

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Section: 2mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%