# Transverse Hilbert schemes and completely integrable systems

Complex Manifolds (2017)

- Volume: 4, Issue: 1, page 263-272
- ISSN: 2300-7443

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topNiccolò Lora Lamia Donin. "Transverse Hilbert schemes and completely integrable systems." Complex Manifolds 4.1 (2017): 263-272. <http://eudml.org/doc/288371>.

@article{NiccolòLoraLamiaDonin2017,

abstract = {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].},

author = {Niccolò Lora Lamia Donin},

journal = {Complex Manifolds},

keywords = {Holomorphic completely integrable systems; Symplectic geometry; Transverse Hilbert schemes},

language = {eng},

number = {1},

pages = {263-272},

title = {Transverse Hilbert schemes and completely integrable systems},

url = {http://eudml.org/doc/288371},

volume = {4},

year = {2017},

}

TY - JOUR

AU - Niccolò Lora Lamia Donin

TI - Transverse Hilbert schemes and completely integrable systems

JO - Complex Manifolds

PY - 2017

VL - 4

IS - 1

SP - 263

EP - 272

AB - 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].

LA - eng

KW - Holomorphic completely integrable systems; Symplectic geometry; Transverse Hilbert schemes

UR - http://eudml.org/doc/288371

ER -

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