A note on the Kähler and Mori cones of hyperkähler manifolds

Mongardi, Giovanni

doi:10.4310/ajm.2015.v19.n4.a1

Cited by 54 publications

(111 citation statements)

References 62 publications

(140 reference statements)

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“…Proposition 2 has been obtained independently by Mongardi [Mon13]. His proof is based on twistor deformations, and also applies to non-projective manifolds.…”

Section: Statement Of Resultsmentioning

confidence: 98%

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Mori cones of holomorphic symplectic varieties of K3 type

Bayer

Hassett

Tschinkel³

2015

Ann. Sci. École Norm. Sup.

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“…Proposition 2 has been obtained independently by Mongardi [Mon13]. His proof is based on twistor deformations, and also applies to non-projective manifolds.…”

Section: Statement Of Resultsmentioning

confidence: 98%

“…We are indebted to the referees for their careful reading of our manuscript. The first author would also like to thank Giovanni Mongardi for discussions and a preliminary version of [Mon13]. Related questions for general hyperkähler manifolds have been treated in [AV14].…”

Section: Acknowledgmentsmentioning

confidence: 99%

Mori cones of holomorphic symplectic varieties of K3 type

Bayer

Hassett

Tschinkel³

2015

Ann. Sci. École Norm. Sup.

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“…After a change of base to

(h_{1}, h_{2}, θ)

we obtain

[\begin{matrix} 0 & 2 & 0 \\ 2 & 0 & 0 \\ 0 & 0 & - 10 \end{matrix}] .

We find that the map

ξ

is given by

h_{1} + h_{2}

. Since there is a divisor with self‐intersection

- 10

and divisibility 2 perpendicular to

h_{1} + h_{2}

, it follows that

ξ

contracts a

P^{2}

to a point (see [, § 5.1] or [, § 2]). We can identify this

P^{2}

as the set of pairs of points on

S_{A}

such that the line spanned by these points is contained in the threefold section of

G (2, 5)

containing

S_{A}

.…”

Section: First Construction — Singular Epw Cubesmentioning

confidence: 98%

Hyper-Kähler fourfolds and Kummer surfaces

Iliev

Kapustka

et al. 2017

Proc. London Math. Soc.

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Abstract. We show that a Hilbert scheme of conics on a Fano fourfold double cover of P 2 × P 2 ramified along a divisor of bidegree (2, 2) admits a P 1 -fibration with base being a hyper-Kähler fourfold. We investigate the geometry of such fourfolds relating them with degenerated EPW cubes, with elements in the Brauer groups of K3 surfaces of degree 2, and with Verra threefolds studied in [Ver04]. These hyper-Kähler fourfolds admit natural involutions and complete the classification of geometric realizations of anti-symplectic involutions on hyper-Kähler 4-folds of type K3 [2] . As a consequence we present also three constructions of quartic Kummer surfaces in P 3 : as Lagrangian and symmetric degeneracy loci and as the base of a fibration of conics in certain threefold quadric bundles over P 1 .

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“…(as the notation suggests, this is the setwise stabilizer of the sublattice Zv ⊂ Γ 5,21 in O(Γ 5,21 ) ∩ O + (4, 21)). Finally, let us discuss the possibility that O + n contains some duality h ∈ O + (4, 21) of the SCFTs that cannot be extended to an element in O(Γ 5,21 ).…”

Section: The Duality Groupmentioning

confidence: 99%

Some comments on symmetric orbifolds of K3

Volpato

2019

J. High Energ. Phys.

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We consider two dimensional N = (4, 4) superconformal field theories in the moduli space of symmetric orbifolds of K3. We complete a classification of the discrete groups of symmetries of these models, conditional to a series of assumptions and with certain restrictions. Furthermore, we provide a partial classification of the set of twining genera, encoding the action of a discrete symmetry g on a space of supersymmetric states in these models. These results suggest the existence of a number of surprising identities between seemingly different Borcherds products, representing Siegel modular forms of degree two and level N > 1. We also provide a critical review of various properties of the moduli space of these superconformal field theories, including the groups of dualities, the set of singular models and the locus of symmetric orbifold points, and describe some puzzles related to our (lack of) understanding of these properties. * volpato@pd.infn.it

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A note on the Kähler and Mori cones of hyperkähler manifolds

Abstract: In the present paper we prove that, on a hyperkähler manifold, walls of the Kähler cone and extremal rays of the Mori cone are determined by all divisors satisfying certain numerical conditions.

Cited by 54 publications

References 62 publications

Mori cones of holomorphic symplectic varieties of K3 type

Mori cones of holomorphic symplectic varieties of K3 type

Hyper-Kähler fourfolds and Kummer surfaces

Some comments on symmetric orbifolds of K3

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