We give combinatorial models for the homotopy type of complements of elliptic arrangements, ie certain sets of abelian subvarieties in a product of elliptic curves. We give a presentation of the fundamental group of such spaces and, as an application, we treat the case of ordered configuration spaces of elliptic curves.Our models are finite polyhedral CW complexes, and our combinatorial tools of choice are acyclic categories (small categories without loops). As a stepping stone, we give a characterization of which acyclic categories arise as face categories of polyhedral CW complexes.

The homotopy type of elliptic arrangements

Delucchi E.;Pagaria R.
2021

Abstract

We give combinatorial models for the homotopy type of complements of elliptic arrangements, ie certain sets of abelian subvarieties in a product of elliptic curves. We give a presentation of the fundamental group of such spaces and, as an application, we treat the case of ordered configuration spaces of elliptic curves.Our models are finite polyhedral CW complexes, and our combinatorial tools of choice are acyclic categories (small categories without loops). As a stepping stone, we give a characterization of which acyclic categories arise as face categories of polyhedral CW complexes.
2021
Delucchi E.; Pagaria R.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11585/832432
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