Massey Products and Fujita decompositions on fibrations of curves

Pirola, Gian Pietro; Torelli, Sara

doi:10.48550/arxiv.1710.02828

Cited by 2 publications

(7 citation statements)

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“…The proof of the first inequality (1.4) follows the lines of the original argument of [BGAN15], but in this more general setting new results are needed. The key points of our arguments are the deformation thecnhniques developed by the first author in [GA16] and by the third author and Pirola in [PT17], together with an ad-hoc Castelnuovo-de Franchis theorem for tubular surfaces.…”

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confidence: 99%

On the rank of the flat unitary summand of the Hodge bundle

González-Alonso

Stoppino

Torelli

2019

Trans. Amer. Math. Soc.

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Let f : S → B f\colon S\to B be a nonisotrivial fibered surface. We prove that the genus g g , the rank u f u_f of the unitary summand of the Hodge bundle f ∗ ω f f_*\omega _f , and the Clifford index c f c_f satisfy the inequality u f ≤ g − c f u_f \leq g - c_f . Moreover, we prove that if the general fiber is a plane curve of degree ≥ 5 \geq 5 , then the stronger bound u f ≤ g − c f − 1 u_f \leq g - c_f-1 holds. In particular, this provides a strengthening of bounds proved by M. A. Barja, V. González-Alonso, and J. C. Naranjo and by F. F. Favale, J. C. Naranjo, and G. P. Pirola. The strongholds of our arguments are the deformation techniques developed by the first author and by the third author and G. P. Pirola, which display here naturally their power and depth.

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confidence: 99%

On the rank of the flat unitary summand of the Hodge bundle

González-Alonso

Stoppino

Torelli

2019

Trans. Amer. Math. Soc.

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“…We consider the bundles U and K of this VHS. In this case both U and K can be described in terms of the submersion f : C → B using holomorphic 1-forms on C. We outline shortly this description, referring to [22] and [11] for details. Let…”

Section: Assume Now That B Is a Riemann Surface And That (Hmentioning

confidence: 99%

“…Secondly, our proof depends heavily on some recent results obtained in [22,11]. In fact starting from the geodesics, we build a complex one-dimensional family of curves (contained in the Y ) and we apply the above-mentioned results to this family.…”

Section: Introductionmentioning

confidence: 99%

“…In fact starting from the geodesics, we build a complex one-dimensional family of curves (contained in the Y ) and we apply the above-mentioned results to this family. This allows to split the proof in two cases: in the first case one of the main theorems in [22,11] yields a map of the whole family onto a fixed curve. From this one easily gets a better bound on dim Y .…”

Section: Introductionmentioning

confidence: 99%

“…The plan of the paper is the following: in §2 we recall some definitions and some results from [22,11]. In §3 we study the relation of geodesics to Hodge theory.…”

Section: Introductionmentioning

confidence: 99%

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