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Let $X$ be a smooth complex projective variety of dimension $n\geq2$, let $\mathfrak{E}=(E,\varphi)$ be a Higgs bundle over $X$ of rank $r\geq2$.
Does exists a Higgs quotient sheaf $\mathcal{Q}$ of $\mathfrak{E}$ of rank $p$, for any $p\in\{1,\dotsc,r-1\}$?
For clarity: Higgs sheaf $\mathfrak{E...
In mathematics, a Higgs bundle is a pair
(
E
,
φ
)
{\displaystyle (E,\varphi )}
consisting of a holomorphic vector bundle E and a Higgs field
φ
{\displaystyle \varphi }
, a holomorphic 1-form taking values in End(E) such that
φ
∧
φ
=
0
{\displaystyle \varphi \wedge \varphi =0}
. Such pairs were introduced by Nigel Hitchin (1987), who named the field
φ
{\displaystyle...
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