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Izvestiya: Mathematics, 2010, Volume 74, Issue 5, Pages 883–923
DOI: https://doi.org/10.1070/IM2010v074n05ABEH002511 (Mi im2795) 		 
On embeddings of universal torsors over del Pezzo surfaces in cones over flag varieties

V. S. Zhgoonab

a Scientific Research Institute for System Studies of RAS
b Laboratoire J.-V. Poncelet, Independent University of Moscow
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DOI: https://doi.org/10.1070/IM2010v074n05ABEH002511
Abstract: Following Skorobogatov and Serganova, we construct embeddings of universal torsors over del Pezzo surfaces in cones over flag varieties regarded as closed orbits in the projectivizations of quasi-miniscule representations. Our approach enables us to construct embeddings of universal torsors over del Pezzo surfaces of degree 1. This approach uses the notion of Mumford stability and differs slightly from that of the authors named above.
Keywords: miniscule representation, del Pezzo surface, universal torsor, Mumford quotient.
Received: 25.04.2008
Revised: 05.02.2010
Russian version:
Izvestiya Rossiiskoi Akademii Nauk. Seriya Matematicheskaya, 2010, Volume 74, Issue 5, Pages 3–44
DOI: https://doi.org/10.4213/im2795
Bibliographic databases:
Document Type: Article
UDC: 512.745.2
MSC: 14L30, 14M17
Language: English
Original paper language: Russian
Citation: V. S. Zhgoon, “On embeddings of universal torsors over del Pezzo surfaces in cones over flag varieties”, Izv. RAN. Ser. Mat., 74:5 (2010), 3–44; Izv. Math., 74:5 (2010), 883–923
Citation in format AMSBIB
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    		Известия Российской академии наук. Серия математическая Izvestiya: Mathematics
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