Bruzzo’s Conjecture

“…The existence of semistable Higgs bundles is related to a conjecture which was established in [5] (see [10] for a review). The conjecture is about an extension of the following result, first proved in Date: September 24, 2018 2000 Mathematics Subject Classification: 14F05, 14H60, 14J60 Keywords: Higgs bundles, Bogomolov inequality, restriction to curves, K3 surfaces Email: bruzzo@sissa.it, valeriano@ime.unicamp.br, alessiologiudic@gmail.com [12], which generalizes to higher dimensions Miyaoka's semistability criterion for bundles on curves [11].…”

Section: Introductionmentioning

confidence: 96%

Semistable Higgs bundles on Calabi-Yau manifolds

Bruzzo¹,

Lanza²,

Giudice³

2017

Preprint

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On a Conjecture About Higgs Bundles and Some Inequalities

Bruzzo,

Graña Otero,

Hernández Ruipérez

2023

Mediterr. J. Math.

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We briefly review an open conjecture about Higgs bundles that are semistable after pulling back to any curve, and prove it in the rank 2 case. We also prove some results in higher rank under suitable additional assumptions. Moreover, we establish a set of inequalities holding for H-nef Higgs bundles that generalize some of the Fulton–Lazarsfeld inequalities for numerically effective vector bundles.

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Bruzzo’s Conjecture

Cited by 5 publications

References 15 publications

Semistable Higgs bundles on Calabi–Yau manifolds

Semistable Higgs bundles on Calabi–Yau manifolds

Semistable Higgs bundles on Calabi-Yau manifolds

On a Conjecture About Higgs Bundles and Some Inequalities

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