scholarly journals Ramified covers and tame isomonodromic solutions on curves

2015 ◽  
Vol 76 ◽  
pp. 219-236
Author(s):  
Karamoko Diarra ◽  
Frank Loray
Keyword(s):  
Ramified Covers

scholarly journals ALGEBRAIC FIBER SPACES AND CURVATURE OF HIGHER DIRECT IMAGES

2020 ◽  
pp. 1-56
Author(s):  
Bo Berndtsson ◽  
Mihai Păun ◽  
Xu Wang
Keyword(s):  
Line Bundle ◽  
Open Subset ◽  
Fiber Space ◽  
Zariski Open Subset ◽  
Negatively Curved ◽  
Ramified Covers

Let $p:X\rightarrow Y$ be an algebraic fiber space, and let $L$ be a line bundle on $X$ . In this article, we obtain a curvature formula for the higher direct images of $\unicode[STIX]{x1D6FA}_{X/Y}^{i}\otimes L$ restricted to a suitable Zariski open subset of $X$ . Our results are particularly meaningful if $L$ is semi-negatively curved on $X$ and strictly negative or trivial on smooth fibers of $p$ . Several applications are obtained, including a new proof of a result by Viehweg–Zuo in the context of a canonically polarized family of maximal variation and its version for Calabi–Yau families. The main feature of our approach is that the general curvature formulas we obtain allow us to bypass the use of ramified covers – and the complications that are induced by them.

scholarly journals On ramified covers of the projective plane II: Generalizing Segre’s theory

2012 ◽  
pp. 971-996
Author(s):  
Michael Friedman ◽  
Mina Teicher ◽  
Rebecca Lehman ◽  
Maxim Leyenson
Keyword(s):  
Projective Plane ◽  
Ramified Covers

scholarly journals Double Kodaira fibrations with small signature

2020 ◽  
Vol 31 (07) ◽  
pp. 2050052 ◽  
Author(s):  
Ju A Lee ◽  
Michael Lönne ◽  
Sönke Rollenske
Keyword(s):  
General Type ◽  
Fiber Bundles ◽  
Surfaces Of General Type ◽  
Positive Signature ◽  
Fix Point ◽  
Ramified Covers

Kodaira fibrations are surfaces of general type with a non-isotrivial fibration, which are differentiable fiber bundles. They are known to have positive signature divisible by [Formula: see text]. Examples are known only with signature 16 and more. We review approaches to construct examples of low signature which admit two independent fibrations. Special attention is paid to ramified covers of product of curves which we analyze by studying the monodromy action for bundles of punctured curves. As a by-product, we obtain a classification of all fix-point-free automorphisms on curves of genus at most [Formula: see text].

scholarly journals Galois action on homology of generalized Fermat Curves

2020 ◽  
Vol 71 (4) ◽  
pp. 1377-1417
Author(s):  
Aristides Kontogeorgis ◽  
Panagiotis Paramantzoglou
Keyword(s):  
Fundamental Group ◽  
Galois Group ◽  
Projective Line ◽  
Galois Groups ◽  
Absolute Galois Group ◽  
Burau Representation ◽  
Galois Action ◽  
Unified Study ◽  
Fermat Curves ◽  
Ramified Covers

Abstract The fundamental group of Fermat and generalized Fermat curves is computed. These curves are Galois ramified covers of the projective line with abelian Galois groups H. We provide a unified study of the action of both cover Galois group H and the absolute Galois group $\mathrm{Gal}(\bar{\mathbb{Q}}/\mathbb{Q})$ on the pro-$\ell$ homology of the curves in study. Also the relation to the pro-$\ell$ Burau representation is investigated.

Conductors of wildly ramified covers, I

2002 ◽  
Vol 335 (5) ◽  
pp. 481-484 ◽  
Author(s):  
Rachel J Pries
Keyword(s):  
Ramified Covers
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