Scholarlink

<p>We study parabolic bundles on an algebraic curve in positive characteristic. Our motivation is to properly formulate Frobenius pull-backs of parabolic bundles in a way that extends various previous facts and arguments for the usual non-parabolic Frobenius pull-backs. After defining that operation, we generalize a classical result by Cartier concerning Frobenius descent, that is, we establish a bijective correspondence (including the version using higher-level <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="12044_2025_824_Article_IEq1.gif" Format="GIF" Height="14" Rendition="HTML" Resolution="72" Type="Linedraw" Width="18" /> </InlineMediaObject> <EquationSource Format="TEX">\(\mathcal {D}\)</EquationSource> <EquationSource Format="MATHML"><math> <mi mathvariant="script">D</mi> </math></EquationSource> </InlineEquation>-modules) between parabolic flat bundles with vanishing <i>p</i>-curvature on a pointed curve and parabolic bundles on its Frobenius twist. This correspondence gives a description of maximally Frobenius-destabilized parabolic bundles in terms of dormant opers admitting logarithmic poles. As an application of that description together with a previous result in the enumerative geometry of dormant opers, we obtain an explicit formula for computing the number of such parabolic bundles of rank 2 under certain assumptions.</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

Frobenius Pull-Back of Parabolic Bundles and Dormant Opers

  • 期刊论文

  • 发表日期：

    2025年8月23日

查看全文
  • Yasuhiro Wakabayashi

摘要

We study parabolic bundles on an algebraic curve in positive characteristic. Our motivation is to properly formulate Frobenius pull-backs of parabolic bundles in a way that extends various previous facts and arguments for the usual non-parabolic Frobenius pull-backs. After defining that operation, we generalize a classical result by Cartier concerning Frobenius descent, that is, we establish a bijective correspondence (including the version using higher-level \(\mathcal {D}\) D -modules) between parabolic flat bundles with vanishing p-curvature on a pointed curve and parabolic bundles on its Frobenius twist. This correspondence gives a description of maximally Frobenius-destabilized parabolic bundles in terms of dormant opers admitting logarithmic poles. As an application of that description together with a previous result in the enumerative geometry of dormant opers, we obtain an explicit formula for computing the number of such parabolic bundles of rank 2 under certain assumptions.