Strict monotonicity conjecture for Mori flips

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Let g ⁣:X⇢X+g\colon X\dashrightarrow X^+ be a birational morphism between [200 Q[200~\mathbb{Q}-Gorenstein varieties, together with birational morphisms f ⁣:X→Zf\colon X\to Z and f+ ⁣:X+→Zf^+\colon X^+\to Z, such that gg is an isomorphism in codimension one, −KX-K_X is ff-ample, and KX+K_{X^+} is f+f^+-ample; such a transformation is called a Mori flip. Strict monotonicity conjecture.

ealgstr(X)>ealgstr(X+).e^{\rm str}_{\rm alg}(X)>e^{\rm str}_{\rm alg}(X^+).

This is the flip case of the proposed strict monotonicity of the algebraic stringy Euler number under elementary birational transformations in the Mori program; the source does not state whether it has been resolved.

References

Primary source

Victor Batyrev and Giuliano Gagliardi, “On the algebraic stringy Euler number”, arXiv:1610.03842 (2017).

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