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February 28, 2026Algebra Colloquium0 citations

Moduli Space of Parabolic Bundles on P 1 and Frobenius Splitting

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YZYanglong Zhang

Key Points

  • The aim is to investigate the F-splitting of the moduli space of parabolic bundles and to address a conjecture by Mehta and Ramadas.
  • Defined a finite set of points in an algebraically closed field.
  • Examined the moduli space of semistable parabolic bundles of rank two and specific degrees.
  • Proved conditions under which the moduli space exhibits F-splitting.
  • Establishes that the moduli space is F-split for specific conditions on weights and degrees.
  • Partially resolves the conjecture concerning the genus zero case by confirming F-splitting.

Abstract

Let Formula: see text be a finite set of Formula: see text over an algebraically closed field Formula: see text of Formula: see text, and Formula: see text be the moduli space of semistable parabolic bundles of rank two and degree Formula: see text on Formula: see text with parabolic structures determined by weights Formula: see text. We prove that Formula: see text is F-split when Formula: see text, which partly answers a conjecture of Mehta and Ramadas for the genus zero case.

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Cite This Study

Yanglong Zhang (2026) studied this question.

synapsesocial.com/papers/69a288060a974eb0d3c03fcbhttps://doi.org/10.1142/s1005386726000052
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