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Punctual characterization of the unitary flat bundle of weight 1 PVHS and application to families of curves
- Publication Year :
- 2021
-
Abstract
- In this paper we consider the problem of pointwise determining the fibres of the flat unitary subbundle of a PVHS of weight one. Starting from the associated Higgs field, and assuming the base has dimension $1$, we construct a family of (smooth but possibly non-holomorphic) morphisms of vector bundles with the property that the intersection of their kernels at a general point is the fibre of the flat subbundle. We explore the first one of these morphisms in the case of a geometric PVHS arising from a family of smooth projective curves, showing that it acts as the cup-product with some sort of "second-order Kodaira-Spencer class" which we introduce, and check in the case of a family of smooth plane curves that this additional condition is non-trivial.<br />Comment: Title changed to emphasize the contents of the first sections
- Subjects :
- Mathematics - Algebraic Geometry
Subjects
Details
- Database :
- arXiv
- Publication Type :
- Report
- Accession number :
- edsarx.2101.03153
- Document Type :
- Working Paper