Normalized Berkovich spaces and surface singularities

DOI10.1090/tran/7209zbMath1423.14171OpenAlexW2292903622MaRDI QIDQ4586331

Lorenzo Fantini

Publication date: 13 September 2018

Published in: Transactions of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1090/tran/7209

Mathematics Subject Classification ID

Singularities in algebraic geometry (14B05) Global theory and resolution of singularities (algebro-geometric aspects) (14E15) Singularities of surfaces or higher-dimensional varieties (14J17) Rigid analytic geometry (14G22)

Related Items

Inner geometry of complex surfaces: a valuative approach, On Lipschitz normally embedded complex surface germs, Topology of spaces of valuations and geometry of singularities, Local dynamics of non-invertible maps near normal surface singularities, Degenerations of \(\mathrm{SL}(2, \mathbb{C})\) representations and Lyapunov exponents, Links of sandwiched surface singularities and self-similarity, Ultrametric properties for valuation spaces of normal surface singularities, Degenerated Calabi-Yau varieties with infinite components, moduli compactifications, and limit toroidal structures, On the homeomorphism type of some spaces of valuations

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Normalized non-Archimedean links and surface singularities
• Sur les espaces de Stein quasi-compacts en géométrie rigide. (On quasi-compact Stein spaces in rigid geometry)
• Stable reduction and uniformization of abelian varieties. I
• Valuations and plurisubharmonic singularities
• Basic deformation theory of smooth formal schemes
• A trace formula for rigid varieties, and motivic Weil generating series for formal schemes
• Formal and rigid geometry: an intuitive introduction and some applications
• Local uniformization on algebraic surfaces over ground fields of characteristic \(p\neq 0\)
• On the excellent property for power series rings over polynomial rings
• Eine bemerkenswerte Eigenschaft der formellen Fasern affinoider Räume
• Formal and rigid geometry. I: Rigid spaces
• Vanishing cycles for formal schemes
• Étale cohomology for non-Archimedean analytic spaces
• Parties semi-algébriques d'une variété algébrique \(p\)-adique. (Semi-algebraic subsets of a \(p\)-adic algebraic variety.)
• The valuative tree
• Arc structure of singularities
• Crystalline Dieudonné module theory via formal and rigid geometry
• Vanishing cycles for formal schemes. II
• The Nash problem for surfaces
• Berkovich spaces and tubular descent
• Every tamely ramified form of an open polydisc is trivial
• Berkovich spaces, polytopes, skeleton, and model theory
• Valuations and asymptotic invariants for sequences of ideals
• Analytic functions on tubes of nonarchimedean analytic spaces
• Lectures on formal and rigid geometry
• Jacobian discrepancies and rational singularities
• Toward a numerical theory of ampleness
• Über die Methode der diskret bewerteten Rigne in der nicht- archimedischen Analysis
• Éléments de géométrie algébrique. IV: Étude locale des schémas et des morphismes de schémas (Quatrième partie). Rédigé avec la colloboration de J. Dieudonné
• Über Modifikationen und exzeptionelle analytische Mengen
• Algebraization of formal moduli. II: Existence of modifications
• Rational singularities, with applications to algebraic surfaces and unique factorization
• Theorem A und B in der nichtarchimedischen Funktionentheorie
• Algebraic spaces
• A new proof of the Gerritzen-Grauert theorem
• Éléments de géométrie algébrique. I: Le langage des schémas. II: Étude globale élémentaire de quelques classe de morphismes. III: Étude cohomologique des faisceaux cohérents (première partie)
• Toroidal geometry and non-archimedean analytic geometry. Application to the homotopy type of certain formal schemes
• On the structure of non-archimedean analytic curves
• Valuation spaces and multiplier ideals on singular varieties
• Singular cohomology of the analytic Milnor fiber, and mixed Hodge structure on the nearby cohomology
• Some Numerical Criteria for Contractability of Curves on Algebraic Surfaces
• Deformation Theory
• A few theorems on completion of excellent rings
• The dual complex of singularities
• Topology of nonarchimedean analytic spaces and relations to complex algebraic geometry
• Introduction to Berkovich Analytic Spaces
• Three-dimensional counter-examples to the Nash problem
• Links of complex analytic singularities
• On the Structure and Ideal Theory of Complete Local Rings