The Morrison–Kawamata cone conjecture for singular symplectic varieties

• Christian Lehn ^[3] ; Giovanni Mongardi ^[1] ; Gianluca Pacienza ^[2]
  1. [1] University of Bologna

     University of Bologna

     Bolonia, Italia

     
  2. [2] University of Lorraine

     University of Lorraine

     Arrondissement de Nancy, Francia

     
  3. [3] Fakultät für Mathematik, Ruhr–Universität Bochum, Germany

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• Localización: Selecta Mathematica, New Series, ISSN 1022-1824, Vol. 30, Nº. 4, 2024, págs. 1-36
• Idioma: inglés
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  • We prove the Morrison–Kawamata cone conjecture for projective primitive symplectic varieties with Q-factorial and terminal singularities with b2 ≥ 5, from which we derive for instance the finiteness of minimal models of such varieties, up to isomorphisms. To prove the conjecture we establish along the way some results on the monodromy group which may be interesting in their own right, such as the fact that reflections in prime exceptional divisors are integral Hodge monodromy operators which, together with monodromy operators provided by birational transformations, yield a semidirect product decomposition of the monodromy group of Hodge isometries.