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Linearization of holomorphic families of algebraic automor- phisms of the affine plane 

Kuroda, S.; Kutzschebauch, F.; Pelka, T.R.Autoridad BCAM (2022-01-03)
Let $G$ be a reductive group. We prove that a family of polynomial actions of $G$ on $\mathbb{C}^2$, holomorphically parametrized by an open Riemann surface, is linearizable. As an application, we show that a particular ...
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Lower bounds on Hilbert-Kunz multiplicities and maximal F-signature 

Jeffries, J.; Nakajima, Y.; Smirnov, I.; Watanabe, K.; Yoshida, K. (2022)
ABSTRACT. Hilbert–Kunz multiplicity and F-signature are numerical invariants of commutative rings in positive characteristic that measure severity of singularities: for a regular ring both invariants are equal to one and ...
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Uniform Lech's inequality 

Ma, L.; Smirnov, I. (2022)
Let (R,m) be a Noetherian local ring of dimension d ≥ 2. We prove that if e(R􏰊red) > 1, then the classical Lech’s inequality can be improved uniformly for all m-primary ideals, that is, there exists ε > 0 such that e(I) ...
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COHOMOLOGY OF CONTACT LOCI 

Budur, N.Autoridad BCAM; Fernández de Bobadilla, J.Autoridad BCAM; Le, Q.; Nguyen, D. (2022-01-01)
We construct a spectral sequence converging to the cohomology with compact support of the m-th contact locus of a complex polynomial. The first page is explicitly described in terms of a log resolution and coincides with ...
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Classification of smooth factorial affine surfaces of Kodaira dimension zero with trivial units 

Pełka, T.; Raźny, P. (2021-07-31)
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 ...
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Image Milnor Number Formulas for Weighted-Homogeneous Map-Germs 

Pallarés Torres, I.Autoridad BCAM; Peñafort Sanchis, Guillermo (2021-07-05)
We give formulas for the image Milnor number of a weighted-homogeneous map-germ $(\mathbb{C}^n,0)\to(\mathbb{C}^{n+1},0)$, for $n=4$ and $5$, in terms of weights and degrees. Our expressions are obtained by a purely ...
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Some contributions to the theory of singularities and their characteristic classes 

Pallarés Torres, I.Autoridad BCAM (2021-06-02)
In this Ph.D. thesis, we give some contributions to the theory of singularities, as well as to the theory of characteristic classes of singular spaces. The first part of this thesis is devoted to the theory of singularities ...
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The Abel map for surface singularities III: Elliptic germs 

Nagy, J.; Némethi, A.Autoridad BCAM (2021-01-01)
The 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, ...
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Delta invariant of curves on rational surfaces I. An analytic approach 

Cogolludo-Agustín, J.I.; László, T.; Martín-Morales, J.; Némethi, A.Autoridad BCAM (2021-01-01)
We prove that if (C, 0) is a reduced curve germ on a rational surface singularity (X, 0) then its delta invariant can be recovered by a concrete expression associated with the embedded topological type of the pair C X. ...
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Moderately Discontinuous Homology 

Fernández de Bobadilla, J.Autoridad BCAM; Heinze, S.; Sampaio, J.E. (2021-01-01)
We introduce a new metric homology theory, which we call Moderately Discontinuous Homology, designed to capture Lipschitz properties of metric singular subanalytic germs. The main novelty of our approach is to allow ...
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EgileaSampaio, J.E. (13)Fernández de Bobadilla, J. (10)Dan, A. (9)Némethi, A. (7)László, T. (6)Nagy, J. (5)Thuong, L.Q. (5)Fernandes, A. (4)Kaur, I. (4)Nguyen, H.D. (4)... másMateriaAbel map (3)mapping class group (3)Multiplicity (3)Picard group (3)rational homology sphere (3)Seiberg-Witten invariants (3)Brill–Noether theory (2)Definable sets (2)Formal schemes (2)Image Milnor number (2)... másFecha2022 (4)2021 (6)2020 (11)2019 (14)2018 (15)2017 (17)2016 (2)

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