Filtered $A$-infinity structures in complex geometry
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- by Joana Cirici and Anna Sopena-Gilboy
- Proc. Amer. Math. Soc. 150 (2022), 4067-4082
- DOI: https://doi.org/10.1090/proc/16009
- Published electronically: June 10, 2022
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Abstract:
We prove a filtered version of the Homotopy Transfer Theorem which gives an $A$-infinity algebra structure on any page of the spectral sequence associated to a filtered dg-algebra. We then develop various applications to the study of the geometry and topology of complex manifolds, using the Hodge filtration, as well as to complex algebraic varieties, using mixed Hodge theory.References
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Bibliographic Information
- Joana Cirici
- Affiliation: Departament de Matemàtiques i Informàtica, Universitat de Barcelona, Gran Via 585, 08007 Barcelona, Spain; and Centre de Recerca Matemàtica, Edifici C, Campus Bellaterra, 08193 Bellaterra, Spain
- MR Author ID: 1061106
- ORCID: 0000-0001-5632-9479
- Email: jcirici@ub.edu
- Anna Sopena-Gilboy
- Affiliation: Departament de Matemàtiques i Informàtica, Universitat de Barcelona, Gran Via 585, 08007 Barcelona, Spain
- Email: asopenagilboy@ub.edu
- Received by editor(s): November 13, 2020
- Received by editor(s) in revised form: November 27, 2021
- Published electronically: June 10, 2022
- Additional Notes: The first author acknowledges the Serra Húnter Program. Her work was also partially funded by the Spanish State Research Agency (María de Maeztu Program CEX2020-001084-M and I+D+i project PID2020-117971GB-C22/MCIN/AEI/10.13039/501100011033) as well as by the French National Research Agency (ANR-20-CE40-0016).
- Communicated by: Julie Bergner
- © Copyright 2022 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 150 (2022), 4067-4082
- MSC (2020): Primary 55P15, 53C15, 32S35
- DOI: https://doi.org/10.1090/proc/16009
- MathSciNet review: 4446252