Browsing Singularity Theory and Algebraic Geometry by Title
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Classification of smooth factorial affine surfaces of Kodaira dimension zero with trivial units
(20210731)We give a corrected statement of (Gurjar and Miyanishi 1988, Theorem 2), which classifies smooth affine surfaces of Kodaira dimension zero, whose coordinate ring is factorial and has trivial units. Denote the class of such ... 
Combinatorial duality for Poincaré series, polytopes and invariants of plumbed 3manifolds
(201806)Assume that the link of a complex normal surface singularity is a rational homology sphere. Then its SeibergWitten invariant can be computed as the ‘periodic constant’ of the topological multivariable Poincaré series (zeta ... 
Criterion for logarithmic connections with prescribed residues
(20170401)A theorem of Weil and Atiyah says that a holomorphic vector bundle $E$ on a compact Riemann surface $X$ admits a holomorphic connection if and only if the degree of every direct summand of $E$ is zero. Fix a finite subset ... 
Decomposition theorem and torus actions of complexity one
(2020)We algorithmically compute the intersection cohomology Betti numbers of any complete normal algebraic variety with a torus action of complexity one. 
Equisingularity in OneParameter Families of Generically Reduced Curves
(20160101)We explore some equisingularity criteria in oneparameter families of generically reduced curves. We prove the equivalence between Whitney regularity and Zariski’s discriminant criterion. We prove that topological triviality ... 
Equivariant motivic integration and proof of the integral identity conjecture for regular functions
(20191202)We develop DenefLoeser’s motivic integration to an equivariant version and use it to prove the full integral identity conjecture for regular functions. In comparison with Hartmann’s work, the equivariant Grothendieck ... 
Euler reflexion formulas for motivic multiple zeta functions
(20170514)We introduce a new notion of $\boxast$product of two integrable series with coefficients in distinct Grothendieck rings of algebraic varieties, preserving the integrability of and commuting with the limit of rational ... 
Examples of varieties with index one on C1 fields
(20190416)Let K be the fraction field of a Henselian discrete valuation ring with algebraically closed residue field k. In this article we give a sufficient criterion for a projective variety over such a field to have index 1. 
General têteàtête graphs and Seifert manifolds
(20180210)Têteàtête graphs and relative têteàtête graphs were introduced by N. A’Campo in 2010 to model monodromies of isolated plane curves. By recent work of Fdez de Bobadilla, Pe Pereira and the author, they provide a way ... 
Globally subanalytic CMC surfaces in $\mathbb{R}^3$ with singularities
(20200302)In this paper we present a classification of a class of globally subanalytic CMC surfaces in $\mathbb{R}^3$ that generalizes the recent classification made by Barbosa and do Carmo in 2016. We show that a globally subanalytic ... 
Hölder equivalence of complex analytic curve singularities
(20180806)We prove that if two germs of irreducible complex analytic curves at $0\in\mathbb{C}^2$ have different sequence of characteristic exponents, then there exists $0<\alpha<1$ such that those germs are not $\alpha$H\"older ... 
Homogeneous singularity and the Alexander polynomial of a projective plane curve
(20171210)The Alexander polynomial of a plane curve is an important invariant in global theories on curves. However, it seems that this invariant and even a much stronger one the fundamental group of the complement of a plane curve ... 
Image Milnor Number Formulas for WeightedHomogeneous MapGerms
(20210705)We give formulas for the image Milnor number of a weightedhomogeneous mapgerm $(\mathbb{C}^n,0)\to(\mathbb{C}^{n+1},0)$, for $n=4$ and $5$, in terms of weights and degrees. Our expressions are obtained by a purely ... 
A jacobian module for disentanglements and applications to Mond's conjecture
(2019)Let $f:(\mathbb C^n,S)\to (\mathbb C^{n+1},0)$ be a germ whose image is given by $g=0$. We define an $\mathcal O_{n+1}$module $M(g)$ with the property that $\mathscr A_e$$\operatorname{codim}(f)\le \dim_\mathbb C M(g)$, ... 
Katomatsumototype results for disentanglements
(2020)We consider the possible disentanglements of holomorphic map germs f : (Cn, 0) → (CN , 0), 0 < n < N, with nonisolated locus of instability Inst(f). The aim is to achieve lower bounds for their (homological) connectiv ity ... 
A LêGreuel type formula for the image Milnor number
(201902)Let $f\colon (\mathbb{C}^n,0)\to (\mathbb{C}^{n+1},0)$ be a corank 1 finitely determined map germ. For a generic linear form $p\colon (\mathbb{C}^{n+1},0)\to(\mathbb{C},0)$ we denote by $g\colon (\mathbb{C}^{n1},0)\to ... 
Local Topological Obstruction For Divisors
(2020)Given a smooth, projective variety $X$ and an effective divisor $D\,\subseteq\, X$, it is wellknown that the (topological) obstruction to the deformation of the fundamental class of $D$ as a Hodge class, lies in ... 
Logarithmic connections on principal bundles over a Riemann surface
(2017)Let $E_G$ be a holomorphic principal $G$bundle on a compact connected Riemann surface $X$, where $G$ is a connected reductive complex affine algebraic group. Fix a finite subset $D\, \subset\, X$, and for each $x\,\in\, ...