scholarly journals Complex Surface Singularities with Rational Homology Disk Smoothings

2021 ◽  
pp. 259-287
Author(s):  
Jonathan Wahl
Keyword(s):  
Complex Surface ◽  
Rational Homology ◽  
Surface Singularities

scholarly journals The Abel map for surface singularities III: Elliptic germs

2021 ◽  
Author(s):  
János Nagy ◽  
András Némethi
Keyword(s):  
General Theory ◽  
Present Note ◽  
Affine Subspace ◽  
Normal Surface ◽  
Rational Homology ◽  
Surface Singularities ◽  
Abel Map ◽  
Appl Math ◽  
Rational Homology Sphere

AbstractThe present note is part of a series of articles targeting the theory of Abel maps associated with complex normal surface singularities with rational homology sphere links (Nagy and Némethi in Math Annal 375(3):1427–1487, 2019; Nagy and Némethi in Adv Math 371:20, 2020; Nagy and Némethi in Pure Appl Math Q 16(4):1123–1146, 2020). Besides the general theory, by the study of specific families we wish to show the power of this new method. Indeed, using the general theory of Abel maps applied for elliptic singularities in this note we are able to prove several key properties for elliptic singularities (e.g. the statements of the next paragraph), which by ‘old’ techniques were not reachable. If $$({\widetilde{X}},E)\rightarrow (X,o)$$ ( X ~ , E ) → ( X , o ) is the resolution of a complex normal surface singularity and $$c_1:{\mathrm{Pic}}({\widetilde{X}})\rightarrow H^2({\widetilde{X}},{\mathbb {Z}})$$ c 1 : Pic ( X ~ ) → H 2 ( X ~ , Z ) is the Chern class map, then $${\mathrm{Pic}}^{l'}({\widetilde{X}}):= c_1^{-1}(l')$$ Pic l ′ ( X ~ ) : = c 1 - 1 ( l ′ ) has a (Brill–Noether type) stratification $$W_{l', k}:= \{{\mathcal {L}}\in {\mathrm{Pic}}^{l'}({\widetilde{X}})\,:\, h^1({\mathcal {L}})=k\}$$ W l ′ , k : = { L ∈ Pic l ′ ( X ~ ) : h 1 ( L ) = k } . In this note we determine it for elliptic singularities together with the stratification according to the cycle of fixed components. E.g., we show that the closure of any $$W(l',k)$$ W ( l ′ , k ) is an affine subspace. 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.

scholarly journals EXPLICIT HORIZONTAL OPEN BOOKS ON SOME PLUMBINGS

2006 ◽  
Vol 17 (09) ◽  
pp. 1013-1031 ◽  
Author(s):  
TOLGA ETGÜ ◽  
BURAK OZBAGCI
Keyword(s):  
Contact Structure ◽  
Complex Surface ◽  
Contact Structures ◽  
Open Book ◽  
Open Books ◽  
Tight Contact ◽  
Weinstein Conjecture ◽  
Circle Bundles ◽  
Surface Singularities

We describe explicit open books on arbitrary plumbings of oriented circle bundles over closed oriented surfaces. We show that, for a non-positive plumbing, the open book we construct is horizontal and the corresponding compatible contact structure is also horizontal and Stein fillable. In particular, on some Seifert fibered 3-manifolds we describe open books which are horizontal with respect to their plumbing description. As another application we describe horizontal open books isomorphic to Milnor open books for some complex surface singularities. Moreover we give examples of tight contact 3-manifolds supported by planar open books. As a consequence, the Weinstein conjecture holds for these tight contact structures [1].

scholarly journals SYMPLECTIC 4-MANIFOLDS VIA SYMPLECTIC SURGERY ON COMPLEX SURFACE SINGULARITIES

2015 ◽  
Vol 52 (4) ◽  
pp. 1213-1223
Author(s):  
HEESANG PARK ◽  
ANDRAS I. STIPSICZ
Keyword(s):  
Complex Surface ◽  
Surface Singularities

scholarly journals Invariants of open books of links of surface singularities

2011 ◽  
Vol 48 (1) ◽  
pp. 135-144
Author(s):  
András Némethi ◽  
Meral Tosun
Keyword(s):  
Contact Structure ◽  
Rational Surface ◽  
Normal Surface ◽  
Rational Homology ◽  
Section 8 ◽  
Open Books ◽  
Binding Number ◽  
Surface Singularities ◽  
Rational Surface Singularities ◽  
Rational Homology Sphere

If M is the link of a complex normal surface singularity, then it carries a canonical contact structure ξcan, which can be identified from the topology of the 3-manifold M. We assume that M is a rational homology sphere. We compute the support genus, the binding number and the norm associated with the open books which support ζcan, provided that we restrict ourselves to the case of (analytic) Milnor open books. In order to do this, we determine monotonity properties of the genus and the Milnor number of all Milnor fibrations in terms of the Lipman cone.We generalize results of [3] valid for links of rational surface singularities, and we answer some questions of Etnyre and Ozbagci [7, section 8] regarding the above invariants.

scholarly journals Complex surface singularities from the combinatorial point of view

1995 ◽  
Vol 66 (3) ◽  
pp. 251-265 ◽  
Author(s):  
Francisco Larrión ◽  
José Seade
Keyword(s):  
Complex Surface ◽  
Point Of View ◽  
Surface Singularities ◽  
Combinatorial Point

The signature of smoothings of complex surface singularities

1978 ◽  
Vol 232 (1) ◽  
pp. 85-98 ◽  
Author(s):  
Alan H. Durfee
Keyword(s):  
Complex Surface ◽  
Surface Singularities

scholarly journals Bi-Lipschitz geometry of complex surface singularities

2008 ◽  
Vol 139 (1) ◽  
pp. 259-267 ◽  
Author(s):  
Lev Birbrair ◽  
Alexandre Fernandes ◽  
Walter D. Neumann
Keyword(s):  
Complex Surface ◽  
Surface Singularities

scholarly journals Complex surface singularities with integral homology sphere links

2005 ◽  
Vol 9 (2) ◽  
pp. 757-811 ◽  
Author(s):  
Walter D Neumann ◽  
Jonathan Wahl
Keyword(s):  
Complex Surface ◽  
Homology Sphere ◽  
Integral Homology ◽  
Surface Singularities

scholarly journals Complex surface singularities and degenerations of compact complex curves

2010 ◽  
Vol 43 (2) ◽  
Author(s):  
Tadashi Tomaru
Keyword(s):  
Complex Surface ◽  
Complex Curves ◽  
Normal Surfaces ◽  
Surface Singularities

AbstractSince 15 years ago, I have been studying some relations between complex normal surfaces ([

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