Algebraic singularities of scattering amplitudes from tropical geometry [PDF]
Journal of High Energy Physics, 2021 We address the appearance of algebraic singularities in the symbol alphabet of scattering amplitudes in the context of planar N $$ \mathcal{N} $$ = 4 super Yang-Mills theory.
James Drummond +3 more
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Singularities of theta divisors in algebraic geometry [PDF]
, 2012 The singularities of theta divisors have played an important role in the study of algebraic varieties. This paper surveys some of the recent progress in this subject, using as motivation some well known results, especially those for Jacobians.
Sebastian Casalaina-Martin
semanticscholar +3 more sources
POWER GEOMETRY IN LOCAL RESOLUTION OF SINGULARITIES OF AN ALGEBRAIC CURVE
World Science, 2020 The main goal of this work is to provide a consistent set of general-purpose algorithms for analyzing singularities applicable to all types of equations.
Akhmadjon Soleev
semanticscholar +3 more sources
Parametric Expansions of an Algebraic Variety near Its Singularities
Axioms, 2023 Presently, there is a method based on Power Geometry that allows one to find asymptotic forms and asymptotic expansions of solutions to different kinds of non-linear equations near their singularities.
Alexander D. Bruno, Alijon A. Azimov
doaj +3 more sources
Inner metric geometry of complex algebraic surfaces with isolated singularities [PDF]
Communications on Pure and Applied Mathematics, 2008 AbstractWe produce examples of complex algebraic surfaces with isolated singularities such that these singularities are not metrically conical, i.e., the germs of the surfaces near singular points are not bi‐Lipschitz equivalent, with respect to the inner metric, to cones.
Lev Birbrair, Alexandre Fernandes
exaly +3 more sources
Landau Singularities Revisited: Computational Algebraic Geometry for Feynman Integrals
Physical Review LettersWe reformulate the analysis of singularities of Feynman integrals in a way that can be practically applied to perturbative computations in the standard model in dimensional regularization. After highlighting issues in the textbook treatment of Landau singularities, we develop an algorithm for classifying and computing them using techniques from ...
Claudia Fevola +2 more
exaly +5 more sources
Landau Singularities Revisited: Computational Algebraic Geometry for Feynman Integrals. [PDF]
Physical Review Letters, 2023 We reformulate the analysis of singularities of Feynman integrals in a way that can be practically applied to perturbative computations in the standard model in dimensional regularization.
Claudia Fevola +2 more
semanticscholar +1 more source
Singularities, Algebraic Geometry, Commutative Algebra, and Related Topics [PDF]
, 2018 exaly +2 more sources
Complex reflection groups and K3 surfaces I [PDF]
Épijournal de Géométrie Algébrique, 2021 We construct here many families of K3 surfaces that one can obtain as quotients of algebraic surfaces by some subgroups of the rank four complex reflection groups. We find in total 15 families with at worst $ADE$--singularities. In particular we classify
Cédric Bonnafé, Alessandra Sarti
doaj +1 more source
Resolution of an algebraic singularity by power geometry algorithms [PDF]
Programming and Computer Software, 2012 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Alexander D. Bruno, Alexander B. Batkhin
openaire +1 more source