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Izv. RAN. Ser. Mat., 2010, Volume 74, Issue 5, Pages 3–44 (Mi izv2795)  

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

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.

DOI: https://doi.org/10.4213/im2795

Full text: PDF file (830 kB)
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English version:
Izvestiya: Mathematics, 2010, 74:5, 883–923

Bibliographic databases:

UDC: 512.745.2
MSC: 14L30, 14M17
Received: 25.04.2008
Revised: 05.02.2010

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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