Transverse Hilbert schemes and completely integrable systems

• Autorzy: Niccolò Lora Lamia Donin
• Języki publikacji: EN

Abstrakty

EN

In this paper we consider a special class of completely integrable systems that arise as transverse Hilbert schemes of d points of a complex symplectic surface S projecting onto ℂ via a surjective map p which is a submersion outside a discrete subset of S. We explicitly endow the transverse Hilbert scheme Sp[d] with a symplectic form and an endomorphism A of its tangent space with 2-dimensional eigenspaces and such that its characteristic polynomial is the square of its minimum polynomial and show it has the maximal number of commuting Hamiltonians.We then provide the inverse construction, starting from a 2ddimensional holomorphic integrable system W which has an endomorphism A: TW → TW satisfying the above properties and recover our initial surface S with W ≌ Sp[d].

Słowa kluczowe

EN

Holomorphic completely integrable systems; Symplectic geometry; Transverse Hilbert schemes

Kategorie tematyczne

• 53C26: Hyper-K\"ahler and quaternionic K\"ahler geometry, ``special'' geometry
• 53D05: Symplectic manifolds, general
• 14C05: Parametrization (Chow and Hilbert schemes)
• 37J35: Completely integrable systems, topological structure of phase space, integration methods

• Wydawca: De Gruyter Open
• Czasopismo: Complex Manifolds
• Rocznik: 2017
• Tom: 4
• Numer: 1
• Strony: 263-272

Daty

wydano

2017-12-20

otrzymano

2017-06-21

zaakceptowano

2017-12-19

online

2017-12-29

Twórcy

autor

Niccolò Lora Lamia Donin

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Identyfikatory

DOI

10.1515/coma-2017-0015