Scholarlink

<p>In this paper, we study Higgs and co-Higgs bundles on non-Kähler elliptic surfaces. We show, in particular, that non-trivial stable Higgs bundles only exist when the base of the elliptic fibration has genus at least two and use this existence result to give explicit topological conditions ensuring the smoothness of moduli spaces of stable rank-2 sheaves on such surfaces. We also show that non-trivial stable co-Higgs bundles only exist when the base of the elliptic fibration has genus 0, in which case the non-Kähler elliptic surface is a Hopf surface. We then give a complete description of non-trivial co-Higgs bundles in the rank 2 case; these non-trivial rank-2 co-Higgs bundles are examples of non-trivial holomorphic Poisson structures on <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="40687_2025_497_Article_IEq1.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="18" /> </InlineMediaObject> <EquationSource Format="TEX">\({\mathbb {P}}^1\)</EquationSource> <EquationSource Format="MATHML"><math> <msup> <mrow> <mi mathvariant="double-struck">P</mi> </mrow> <mn>1</mn> </msup> </math></EquationSource> </InlineEquation>-bundles over Hopf surfaces.</p>

错误：搜索内容不能为空，请输入英文关键词
错误：关键词超出字数限制，请精简
高级检索

(Co)-Higgs bundles on non-Kähler elliptic surfaces

  • 期刊论文

  • 发表日期：

    2025年1月30日

查看全文
  • Eric Boulter,
  • Ruxandra Moraru

摘要

In this paper, we study Higgs and co-Higgs bundles on non-Kähler elliptic surfaces. We show, in particular, that non-trivial stable Higgs bundles only exist when the base of the elliptic fibration has genus at least two and use this existence result to give explicit topological conditions ensuring the smoothness of moduli spaces of stable rank-2 sheaves on such surfaces. We also show that non-trivial stable co-Higgs bundles only exist when the base of the elliptic fibration has genus 0, in which case the non-Kähler elliptic surface is a Hopf surface. We then give a complete description of non-trivial co-Higgs bundles in the rank 2 case; these non-trivial rank-2 co-Higgs bundles are examples of non-trivial holomorphic Poisson structures on \({\mathbb {P}}^1\) P 1 -bundles over Hopf surfaces.