Details
| Originalsprache | Englisch |
|---|---|
| Publikationsstatus | Elektronisch veröffentlicht (E-Pub) - 8 Jan. 2021 |
Abstract
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2021.
Publikation: Arbeitspapier/Preprint › Preprint
}
TY - UNPB
T1 - Punctual characterization of the unitary flat bundle of weight 1 PVHS and application to families of curves
AU - González-Alonso, Víctor
AU - Torelli, Sara
N1 - Title changed to emphasize the contents of the first sections
PY - 2021/1/8
Y1 - 2021/1/8
N2 - 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.
AB - 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.
KW - math.AG
M3 - Preprint
BT - Punctual characterization of the unitary flat bundle of weight 1 PVHS and application to families of curves
ER -