Lagrangian 4-planes in holomorphic symplectic varieties of K3[4]-type

• Autorzy: Benjamin Bakker , Andrei Jorza
• Języki publikacji: EN

Abstrakty

EN

We classify the cohomology classes of Lagrangian 4-planes ℙ4 in a smooth manifold X deformation equivalent to a Hilbert scheme of four points on a K3 surface, up to the monodromy action. Classically, the Mori cone of effective curves on a K3 surface S is generated by nonnegative classes C, for which (C, C) ≥ 0, and nodal classes C, for which (C, C) = −2; Hassett and Tschinkel conjecture that the Mori cone of a holomorphic symplectic variety X is similarly controlled by “nodal” classes C such that (C, C) = −γ, for (·,·) now the Beauville-Bogomolov form, where γ classifies the geometry of the extremal contraction associated to C. In particular, they conjecture that for X deformation equivalent to a Hilbert scheme of n points on a K3 surface, the class C = ℓ of a line in a smooth Lagrangian n-plane ℙn must satisfy (ℓ,ℓ) = −(n + 3)/2. We prove the conjecture for n = 4 by computing the ring of monodromy invariants on X, and showing there is a unique monodromy orbit of Lagrangian 4-planes.

Słowa kluczowe

EN

Holomorphic symplectic variety; Cone of curves

Kategorie tematyczne

• 14J28: K 3 surfaces and Enriques surfaces
• 14G05: Rational points
• 14C25: Algebraic cycles

• Wydawca: De Gruyter Open
• Czasopismo: Open Mathematics
• Rocznik: 2014
• Tom: 12
• Numer: 7
• Strony: 952-975

Daty

wydano

2014-07-01

online

2014-04-03

Twórcy

autor

Benjamin Bakker

• New York University

autor

Andrei Jorza

• University of Notre Dame

Bibliografia

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Identyfikatory

DOI

10.2478/s11533-013-0389-3