Универсальные Абелевы Накрытия Рациональных Особенностей Поверхностей И Мультииндексные Фильтрации

Guseĭn-Zade, S. M.; Дельгадо, Феликс; Delgado, F.; Кампильо, Антонио; Campillo, Antonio

doi:10.4213/faa2897

Cited by 8 publications

(1 citation statement)

References 7 publications

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“…Аналогичным образом можно доказать версии основных утверждений из [4] и [7] для идеалов в кольце функций на рациональной особенности поверхности или на ее универсальном абелевом накрытии. Пусть (S, 0) -рациональная осо-бенность поверхности, и пусть π :…”

Section: пространство эффективных дивизоров наunclassified

Alexander polynomials and Poincaré series of sets of ideals

Guseĭn-Zade¹,

Дельгадо²,

Delgado³

et al. 2011

Функц. анализ и его прил.

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Section: пространство эффективных дивизоров наunclassified

Alexander polynomials and Poincaré series of sets of ideals

Guseĭn-Zade¹,

Дельгадо²,

Delgado³

et al. 2011

Функц. анализ и его прил.

Self Cite

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Combinatorial duality for Poincaré series, polytopes and invariants of plumbed 3-manifolds

Tamás

Nagy²,

Némethi

2019

Sel. Math. New Ser.

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Assume that the link of a complex normal surface singularity is a rational homology sphere. Then its Seiberg-Witten invariant can be computed as the 'periodic constant' of the topological multivariable Poincaré series (zeta function). This involves a complicated regularization procedure (via quasipolynomials measuring the asymptotic behaviour of the coefficients).We show that the (a Gorenstein type) symmetry of the zeta function combined with Ehrhart-Macdonald-Stanley reciprocity (of Ehrhart theory of polytopes) provide a simple expression for the periodic cosntant. Using these dualities we also find a multivariable polynomial generalization of the Seiberg-Witten invariant, and we compute it in terms of lattice points of certain polytopes.All these invariants are also determined via lattice point counting, in this way we establish a completely general topological analogue of formulae of Khovanskii and Morales valid for singularities with non-degenerate Newton principal part.

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The Abel map for surface singularities I: generalities and examples

Nagy¹,

Némethi

2019

Math. Ann.

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If ( X, E) → (X, o) is the resolution of a complex normal surface singularity andIn this note we determine it for elliptic singularities together with the stratification according to the cycle of fixed components. For elliptic singularities we also characterize the End Curve Condition and Weak End Curve Condition in terms of the Abel map, we provide several characterization of them, and finally we show that they are equivalent.

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Универсальные Абелевы Накрытия Рациональных Особенностей Поверхностей И Мультииндексные Фильтрации

Cited by 8 publications

References 7 publications

Alexander polynomials and Poincaré series of sets of ideals

Alexander polynomials and Poincaré series of sets of ideals

Combinatorial duality for Poincaré series, polytopes and invariants of plumbed 3-manifolds

The Abel map for surface singularities I: generalities and examples

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