What question did this study set out to answer?

The aim is to investigate the F-splitting of the moduli space of parabolic bundles and to address a conjecture by Mehta and Ramadas.

February 28, 2026

Moduli Space of Parabolic Bundles on P 1 and Frobenius Splitting

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 (Fri,) studied this question.

synapsesocial.com/papers/69a288060a974eb0d3c03fcb https://doi.org/https://doi.org/10.1142/s1005386726000052

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