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The global derived period map
- Source :
- Advances in Mathematics, Volume 353 (2019), pages 224-280
- Publication Year :
- 2016
-
Abstract
- Abstract. We develop the global period map in the context of derived geometry, generalising Griffiths' classical period map as well as the infinitesimal derived period map. We begin by constructing the derived period domain which classifies Hodge filtrations and enhances the classical period domain. We analyze the monodromy action. Then we associate to any polarized smooth projective map of derived stacks a canonical morphism of derived analytic stacks from the base into the quotient of the derived period domain by monodromy. We conclude the paper by discussing a few examples and a derived Torelli problem. In the appendix we describe how to present derived analytic Artin stacks as hypergroupoids, which may be of independent interest.<br />Comment: 66 pages; removed incorrect statement from appendix and added explicit check that derived period map is well-defined
- Subjects :
- Mathematics - Algebraic Geometry
Subjects
Details
- Database :
- arXiv
- Journal :
- Advances in Mathematics, Volume 353 (2019), pages 224-280
- Publication Type :
- Report
- Accession number :
- edsarx.1607.05984
- Document Type :
- Working Paper
- Full Text :
- https://doi.org/10.1016/j.aim.2019.06.022