Transverse Hilbert schemes and completely integrable systems

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...

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Autor principal:	Donin Niccolò Lora Lamia
Formato:	article
Lenguaje:	EN
Publicado:	De Gruyter 2017
Materias:	holomorphic completely integrable systems symplectic geometry transverse hilbert schemes 53d05 37j35 14c05 53c26 Mathematics QA1-939
Acceso en línea:	https://doaj.org/article/1ac6573f22a8445483d3cca058040122
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spelling	oai:doaj.org-article:1ac6573f22a8445483d3cca0580401222021-12-02T16:36:59ZTransverse Hilbert schemes and completely integrable systems2300-744310.1515/coma-2017-0015https://doaj.org/article/1ac6573f22a8445483d3cca0580401222017-12-01T00:00:00Zhttps://doi.org/10.1515/coma-2017-0015https://doaj.org/toc/2300-7443In 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].Donin Niccolò Lora LamiaDe Gruyterarticleholomorphic completely integrable systemssymplectic geometrytransverse hilbert schemes53d0537j3514c0553c26MathematicsQA1-939ENComplex Manifolds, Vol 4, Iss 1, Pp 263-272 (2017)
institution	DOAJ
collection	DOAJ
language	EN
topic	holomorphic completely integrable systems symplectic geometry transverse hilbert schemes 53d05 37j35 14c05 53c26 Mathematics QA1-939
spellingShingle	holomorphic completely integrable systems symplectic geometry transverse hilbert schemes 53d05 37j35 14c05 53c26 Mathematics QA1-939 Donin Niccolò Lora Lamia Transverse Hilbert schemes and completely integrable systems
description	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].
format	article
author	Donin Niccolò Lora Lamia
author_facet	Donin Niccolò Lora Lamia
author_sort	Donin Niccolò Lora Lamia
title	Transverse Hilbert schemes and completely integrable systems
title_short	Transverse Hilbert schemes and completely integrable systems
title_full	Transverse Hilbert schemes and completely integrable systems
title_fullStr	Transverse Hilbert schemes and completely integrable systems
title_full_unstemmed	Transverse Hilbert schemes and completely integrable systems
title_sort	transverse hilbert schemes and completely integrable systems
publisher	De Gruyter
publishDate	2017
url	https://doaj.org/article/1ac6573f22a8445483d3cca058040122
work_keys_str_mv	AT doninniccololoralamia transversehilbertschemesandcompletelyintegrablesystems
_version_	1718383618051538944

Transverse Hilbert schemes and completely integrable systems

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