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Trudy Matematicheskogo Instituta imeni V.A. Steklova, 2025, Volume 329, Pages 190–208
DOI: https://doi.org/10.4213/tm4466 (Mi tm4466) 		 
Weighted Grassmannians and Their Explicit Description

M. A. Ovcharenkoab

a Steklov Mathematical Institute of Russian Academy of Sciences, ul. Gubkina 8, Moscow, 119991 Russia
b International Laboratory for Mirror Symmetry and Automorphic Forms, HSE University, ul. Usacheva 6, Moscow, 119048 Russia
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DOI: https://doi.org/10.4213/tm4466
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.
Keywords: weighted Grassmannians, weighted projective spaces.
Funding agency Grant number
National Research University Higher School of Economics
The article was prepared within the framework of the HSE University project “International Academic Cooperation.”
Received: January 29, 2025
Revised: May 2, 2025
Accepted: May 5, 2025
Published: 03.09.2025
English version:
Proceedings of the Steklov Institute of Mathematics, 2025, Volume 329, Pages 172–189
DOI: https://doi.org/10.1134/S0081543825600681
Bibliographic databases:
Document Type: Article
Language: Russian
Citation: M. A. Ovcharenko, “Weighted Grassmannians and Their Explicit Description”, Birational Geometry and Fano Varieties, Collected papers. Dedicated to Yuri Gennadievich Prokhorov on the occasion of his 60th birthday, Trudy Mat. Inst. Steklova, 329, Steklov Math. Inst., Moscow, 2025, 190–208; Proc. Steklov Inst. Math., 329 (2025), 172–189
Citation in format AMSBIB
\Bibitem{Ovc25}
\by M.~A.~Ovcharenko
\paper Weighted Grassmannians and Their Explicit Description
\inbook Birational Geometry and Fano Varieties
\bookinfo Collected papers. Dedicated to Yuri Gennadievich Prokhorov on the occasion of his 60th birthday
\serial Trudy Mat. Inst. Steklova
\yr 2025
\vol 329
\pages 190--208
\publ Steklov Math. Inst.
\publaddr Moscow
\mathnet{http://mi.mathnet.ru/tm4466}
\crossref{https://doi.org/10.4213/tm4466}
\transl
\jour Proc. Steklov Inst. Math.
\yr 2025
\vol 329
\pages 172--189
\crossref{https://doi.org/10.1134/S0081543825600681}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-105017160280}
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    		Труды Математического института имени В. А. Стеклова Proceedings of the Steklov Institute of Mathematics
     
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