Complete complexes and spectral sequences

Mikhail Kapranov; Evangelos Routis

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arXiv · 1702.00120

Complete complexes and spectral sequences

Mikhail Kapranov·Evangelos Routis

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Abstract

By analogy with the classical (Chasles-Schubert-Semple-Tyrell) spaces of complete quadrics and complete collineations, we introduce the variety of complete complexes. Its points can be seen as equivalence classes of spectral sequences of a certain type. We prove that the set of such equivalence classes has a structure of a smooth projective variety. We show that it provides a desingularization, with normal crossings boundary, of the Buchsbaum-Eisenbud variety of complexes, i.e., a compactification of the union of its maximal strata.

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Mikhail Kapranov, Evangelos Routis. 2017-02-01. Complete complexes and spectral sequences. https://arxiv.org/abs/1702.00120

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