Extending holomorphic forms from the regular locus of a complex space to a resolution of singularities [PDF]
Journal of The American Mathematical Society, 2020 We investigate under what conditions holomorphic forms defined on the regular locus of a reduced complex space extend to holomorphic (or logarithmic) forms on a resolution of singularities.
Kebekus, Stefan, Schnell, Christian
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Singularities of complex surfaces with solvable local fundamental group
Topology, 1972 P. Wagreich
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Nonlocal vertices and analyticity: Landau equations and general Cutkosky rule
Journal of High Energy Physics, 2018 We study the analyticity properties of amplitudes in theories with nonlocal vertices of the type occurring in string field theory and a wide class of nonlocal field theory models.
Paokuan Chin, E. T. Tomboulis
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The local analytical triviality of a complex analytic singular foliation
Hokkaido Mathematical Journal, 2004 The authors investigate complex analytic singular foliations defined on the complex analytic manifold \(M\) of dimension \(n\). After recalling basic notions of the theory of singular foliations they prove a theorem about local analytic triviality along the leaves. The main tool of the proof is the Whitney stratification of the singular locus. The last
MITERA, Yoshiki, YOSHIZAKI, Junya
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Perfect graphs and complex surface singularities with perfect local fundamental group
Tohoku Mathematical Journal, 1989 An isolated singularity x of a complex surface (X,\({\mathcal O}_ x)\) is \textit{perfect}, or \textit{homological trivial}, if the local fundamental group \(\pi_ 1(\partial U_ x)\) is a perfect group, where \(U_ x\) is a contractible neighborhood of x in X.
Brenton, Lawrence, Drucker, Daniel
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Links of complex analytic singularities [PDF]
, 2013 This is a part survey part research paper studying the local topology of complex analytic spaces. We review and strengthen the results of Kapovich--Koll\'ar "Fundamental groups of links of isolated singularities" (1109.4047) and incorporate the paper ...
Kollár, János
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Singularities and heteroclinic connections in complex-valued evolutionary equations with a quadratic nonlinearity [PDF]
Communications in nonlinear science & numerical simulation, 2021 In this paper, we consider the dynamics of solutions to complex-valued evolutionary partial differential equations (PDEs) and show existence of heteroclinic orbits from nontrivial equilibria to zero via computerassisted proofs.
Jonathan Jaquette +2 more
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The minimal exponent and k-rationality for local complete intersections [PDF]
Journal de l'École polytechnique. Mathématiques, 2022 We show that if $Z$ is a local complete intersection subvariety of a smooth complex variety $X$, of pure codimension $r$, then $Z$ has $k$-rational singularities if and only if $\widetilde{\alpha}(Z)>k+r$, where $\widetilde{\alpha}(Z)$ is the minimal ...
Qianyu Chen, B. Dirks, Mircea Mustactua
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The Poincaré Index on Singular Varieties
J, 2022 In this paper, we discuss a few simple methods for computing the local topological index and its various analogs for vector fields and differential forms given on complex varieties with singularities of different types.
Alexander G. Aleksandrov
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On the vanishing of local homotopy groups for isolated singularities of complex spaces.
Journal für die reine und angewandte Mathematik (Crelles Journal), 1981 H. Hamm
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