On orbits of automorphism groups on horospherical varieties
Viktoriia Borovik
Faculty of Mechanics and Mathematics, Department of Higher Algebra, Lomonosov Moscow State University, Moscow, Russia
Faculty of Computer Science, National Research University Higher School of Economics, Moscow, Russia
Search for more papers by this authorCorresponding Author
Sergey Gaifullin
Faculty of Mechanics and Mathematics, Department of Higher Algebra, Lomonosov Moscow State University, Moscow, Russia
Faculty of Computer Science, National Research University Higher School of Economics, Moscow, Russia
Moscow Center for Fundamental and Applied Mathematic, Moscow, Russia
Correspondence
Sergey Gaifullin, Faculty of Mechanics and Mathematics, Department of Higher Algebra, Lomonosov Moscow State University, Moscow, Russia.
Email: [email protected]
Search for more papers by this authorAnton Shafarevich
Faculty of Mechanics and Mathematics, Department of Higher Algebra, Lomonosov Moscow State University, Moscow, Russia
Faculty of Computer Science, National Research University Higher School of Economics, Moscow, Russia
Moscow Center for Fundamental and Applied Mathematic, Moscow, Russia
Search for more papers by this authorViktoriia Borovik
Faculty of Mechanics and Mathematics, Department of Higher Algebra, Lomonosov Moscow State University, Moscow, Russia
Faculty of Computer Science, National Research University Higher School of Economics, Moscow, Russia
Search for more papers by this authorCorresponding Author
Sergey Gaifullin
Faculty of Mechanics and Mathematics, Department of Higher Algebra, Lomonosov Moscow State University, Moscow, Russia
Faculty of Computer Science, National Research University Higher School of Economics, Moscow, Russia
Moscow Center for Fundamental and Applied Mathematic, Moscow, Russia
Correspondence
Sergey Gaifullin, Faculty of Mechanics and Mathematics, Department of Higher Algebra, Lomonosov Moscow State University, Moscow, Russia.
Email: [email protected]
Search for more papers by this authorAnton Shafarevich
Faculty of Mechanics and Mathematics, Department of Higher Algebra, Lomonosov Moscow State University, Moscow, Russia
Faculty of Computer Science, National Research University Higher School of Economics, Moscow, Russia
Moscow Center for Fundamental and Applied Mathematic, Moscow, Russia
Search for more papers by this authorAbstract
In this paper, we describe orbits of the automorphism group on an affine horospherical variety in terms of degrees of homogeneous with respect to natural grading locally nilpotent derivations. In case of (possibly nonnormal) toric varieties, a description of orbits of the automorphism group in terms of corresponding weight monoid is obtained.
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