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Abstract <p> We propose an explicit construction of a weighted generalised Grassmannian. For a weighted Grassmannian (i.e., for series A) we obtain an effective parametrisation of possible <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="11501_2025_8538_Article_IEq1.gif" Format="GIF" Height="14" Rendition="HTML" Resolution="72" Type="Linedraw" Width="13" /> </InlineMediaObject> <EquationSource Format="TEX">\(\mathbb Z\)</EquationSource> </InlineEquation>-gradings on Plücker coordinates, and provide explicit formulas for its dualising sheaf and Hilbert series in terms of this parametrisation. Our approach can be generalised to other irreducible root systems. </p>

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Weighted Grassmannians and Their Explicit Description

  • 期刊论文

  • 发表日期：

    2025年6月1日

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  • Mikhail Ovcharenko

摘要

Abstract

We propose an explicit construction of a weighted generalised Grassmannian. For a weighted Grassmannian (i.e., for series A) we obtain an effective parametrisation of possible \(\mathbb Z\) -gradings on Plücker coordinates, and provide explicit formulas for its dualising sheaf and Hilbert series in terms of this parametrisation. Our approach can be generalised to other irreducible root systems.