Details
| Original language | English |
|---|---|
| Pages (from-to) | 493-506 |
| Number of pages | 14 |
| Journal | Bulletin of the London Mathematical Society |
| Volume | 53 |
| Issue number | 2 |
| Publication status | Published - 3 Apr 2021 |
Abstract
Cite this
- Standard
- Harvard
- Apa
- Vancouver
- BibTeX
- RIS
In: Bulletin of the London Mathematical Society, Vol. 53, No. 2, 03.04.2021, p. 493-506.
Research output: Contribution to journal › Article › Research › peer review
}
TY - JOUR
T1 - Families of curves with Higgs field of arbitrarily large kernel
AU - González-Alonso, Víctor
AU - Torelli, Sara
N1 - Funding information: During the development of this work, V. González?Alonso was at the Institut für Algebraische Geometrie (Leibniz Universität Hannover). S. Torelli was in Dipartimento di Matematica ‘F. Cassoratti’ (Universit di Pavia), as well as supported by PRIN 2015 Moduli spaces and Lie Theory, INdAM ? GNSAGA, FAR 2016 (PV) Varietà algebriche, calcolo algebrico, grafi orientati e topologici and a Riemann Fellowship (Leibniz Universität Hannover). We want to thank Gian Pietro Pirola for carefully reading previous versions of this work, and spotting an error in the main proof. We also want to thank Lidia Stoppino, Xin Lu and Anand Deopurkar for some very fruitful discussions and enlightening ideas. Sara Torelli also thanks the Riemann Center and the Institute of Algebraic Geometry of Leibniz Universit?t Hannover for their warm hospitality and support during her stay as Riemann Fellow which originated this?work. Open access funding enabled and organized by Projekt DEAL.
PY - 2021/4/3
Y1 - 2021/4/3
N2 - In this article, we consider the flat bundle 풰 and the kernel 풦 of the Higgs field naturally associated to any (polarized) variation of Hodge structures of weight 1. We study how strict the inclusion 풰⊆풦 can be in the geometric case. More precisely, for any smooth projective curve 퐶 of genus 푔⩾2 and any 푟=0,…,푔−1, we construct non-isotrivial deformations of 퐶 over a quasi-projective base such that rk풦=푟 and rk풰⩽푔+12.
AB - In this article, we consider the flat bundle 풰 and the kernel 풦 of the Higgs field naturally associated to any (polarized) variation of Hodge structures of weight 1. We study how strict the inclusion 풰⊆풦 can be in the geometric case. More precisely, for any smooth projective curve 퐶 of genus 푔⩾2 and any 푟=0,…,푔−1, we construct non-isotrivial deformations of 퐶 over a quasi-projective base such that rk풦=푟 and rk풰⩽푔+12.
UR - http://www.scopus.com/inward/record.url?scp=85096706696&partnerID=8YFLogxK
U2 - 10.1112/blms.12437
DO - 10.1112/blms.12437
M3 - Article
AN - SCOPUS:85096706696
VL - 53
SP - 493
EP - 506
JO - Bulletin of the London Mathematical Society
JF - Bulletin of the London Mathematical Society
SN - 0024-6093
IS - 2
ER -