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An elementary description of nef cone for irreducible holomorphic symplectic manifolds
Journal of Geometry and Physics. 2025. Vol. 207. Article 105349.
Anastasia V. Vikulova
We describe MBM classes for irreducible holomorphic symplectic manifolds of K3 and Kummer types. These classes are the monodromy images of extremal rational curves which give the faces of the nef cone of some birational model. We study the connection between our results and A. Bayer and E. Macr\`ı's theory. We apply the numerical method of description due to E. Amerik and M. Verbitsky in low dimensions to the K3 type and Kummer type cases.
Publication based on the results of:
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A B-facet is a lattice -dimensional polytope in the positive octant with a positive normal covector, such that every -dimensional simplex with vertices in it is a B-simplex (i.e., a pyramid of height one with base on a coordinate hyperplane). B-facets were introduced in [2] in the context of the monodromy conjecture. In this paper, we complete the ...
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Added: March 3, 2015
Gritsenko V., Hulek K., Sankaran G., , in: Handbook of Moduli. Vol. IVol. I.: Boston: International Press of Boston Inc, 2013. P. 469–525.
The name "K3 surfaces" was coined by A. Weil in 1957 when he formulated a research programme for these surfaces and theirmoduli. Since then, irreducible holomorphic symplectic manifolds have been introduced as a higher dimensional analogue of K3 surfaces. In this paper we present a review of this theory starting from the definition of K3 ...
Added: March 3, 2015