Let $X$ be a compact connected K"ahler--Einstein manifold with $c_1(TX), geq, 0$. If there is a semistable Higgs vector bundle $(E, , heta)$ on $X$ with $ heta, ot=, 0$, then we show that $c_1(TX)=0$; any $X$ satisfying this condition is called a Calabi--Yau manifold, and it admits a Ricci--flat K"ahler form cite{Ya}. Let $(E, , heta)$ be a polystable Higgs vector bundle on a compact Ricci--flat K"ahler manifold $X$. Let $h$ be an Hermitian structure on $E$ satisfying the Yang--Mills--Higgs equation for $(E, , heta)$. We prove that $h$ also satisfies the Yang--Mills--Higgs equation for $(E, ,0)$. A similar result is proved for Hermitian structures on principal Higgs bundles on $X$ satisfying the Yang--Mills--Higgs equation. © 2016 International Press.

Yang-Mills-Higgs connections on Calabi-Yau manifolds / Biswas, I.; Bruzzo, Ugo; Graña Otero, B.; Lo Giudice, A.. - In: THE ASIAN JOURNAL OF MATHEMATICS. - ISSN 1093-6106. - 20:5(2016), pp. 989-1000. [10.4310/AJM.2016.v20.n5.a8]

Yang-Mills-Higgs connections on Calabi-Yau manifolds

Bruzzo, Ugo;
2016-01-01

Abstract

Let $X$ be a compact connected K"ahler--Einstein manifold with $c_1(TX), geq, 0$. If there is a semistable Higgs vector bundle $(E, , heta)$ on $X$ with $ heta, ot=, 0$, then we show that $c_1(TX)=0$; any $X$ satisfying this condition is called a Calabi--Yau manifold, and it admits a Ricci--flat K"ahler form cite{Ya}. Let $(E, , heta)$ be a polystable Higgs vector bundle on a compact Ricci--flat K"ahler manifold $X$. Let $h$ be an Hermitian structure on $E$ satisfying the Yang--Mills--Higgs equation for $(E, , heta)$. We prove that $h$ also satisfies the Yang--Mills--Higgs equation for $(E, ,0)$. A similar result is proved for Hermitian structures on principal Higgs bundles on $X$ satisfying the Yang--Mills--Higgs equation. © 2016 International Press.
2016
20
5
989
1000
https://arxiv.org/abs/1412.7738
http://cdsads.u-strasbg.fr/abs/2014arXiv1412.7738B
Biswas, I.; Bruzzo, Ugo; Graña Otero, B.; Lo Giudice, A.
File in questo prodotto:
File Dimensione Formato  
1412.7738.pdf

accesso aperto

Tipologia: Documento in Pre-print
Licenza: Non specificato
Dimensione 188.73 kB
Formato Adobe PDF
188.73 kB Adobe PDF Visualizza/Apri

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/20.500.11767/11959
Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 4
  • ???jsp.display-item.citation.isi??? 4
social impact