Foliations of multiprojective spaces and a conjecture of Bernstein and Lunts

Coutinho, S.

doi:10.1090/S0002-9947-2010-05230-4

Foliations of multiprojective spaces and a conjecture of Bernstein and Lunts
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Trans. Amer. Math. Soc. 363 (2011), 2125-2142 Request permission

Abstract:

We use foliations of multiprojective spaces defined by Hamiltonian functions on the underlying affine space to prove the three dimensional case of a conjecture of Bernstein and Lunts, according to which the symbol of a generic first-order differential operator gives rise to a hypersurface of the cotangent bundle which does not contain involutive conical subvarieties apart from the zero section and fibres of the bundle.

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