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4 papers · 1 filter
Flops on holomorphic symplectic fourfolds and determinantal cubic hypersurfaces
Brendan Hassett, Yuri Tschinkel
We study the birational geometry of irreducible holomorphic symplectic varieties arising as varieties of lines of general cubic fourfolds containing a cubic scroll. We compute the…
Moving and ample cones of holomorphic symplectic fourfolds
Brendan Hassett, Yuri Tschinkel
We analyze the ample and moving cones of holomorphic symplectic manifolds, in light of recent advances in the minimal model program. As an application, we establish a numerical cri…
Log Fano varieties over function fields of curves
Brendan Hassett, Yuri Tschinkel
Consider a smooth log Fano variety over the function field of a curve. Suppose that the boundary has positive normal bundle. Choose an integral model over the curve. Then integral…
Rationality of moduli of elliptic fibrations with fixed monodromy
Fedor Bogomolov, Tihomir Petrov, Yuri Tschinkel
We prove rationality results for moduli spaces of elliptic K3 surfaces and elliptic rational surfaces with fixed monodromy groups.