Results 1 to 10 of about 341,235 (326)
Hartogs-type theorems in real algebraic geometry, I [PDF]
Mathematische Annalen, 2022 AbstractLet $$f:X\rightarrow \mathbb {R}$$ f : X → R be a function defined on a connected nonsingular real algebraic set X in $$\mathbb {R}^n$$
Marcin Bilski +2 more
semanticscholar +11 more sources
Formal proofs in real algebraic geometry: from ordered fields to quantifier elimination [PDF]
Logical Methods in Computer Science, 2012 This paper describes a formalization of discrete real closed fields in the Coq proof assistant. This abstract structure captures for instance the theory of real algebraic numbers, a decidable subset of real numbers with good algorithmic properties.
Assia Mahboubi, Cyril Cohen
doaj +4 more sources
Noncommutative real algebraic geometry of Kazhdan's property (T) [PDF]
Journal of the Institute of Mathematics of Jussieu, 2015 It is well-known that a finitely generated group $\Gamma$ has Kazhdan's property (T) if and only if the Laplacian element $\Delta$ in ${\mathbb R}[\Gamma]$ has a spectral gap.
Ozawa, Narutaka
core +8 more sources
Integral closures in real algebraic geometry [PDF]
Journal of Algebraic Geometry, 2020 We study the algebraic and geometric properties of the integral closure of different rings of functions on a real algebraic variety: the regular functions and the continuous rational functions.
Goulwen Fichou +2 more
semanticscholar +8 more sources
Dequantization of real algebraic geometry on logarithmic paper [PDF]
, 2000 12 pages, 3 figures, Plenary talk at the 3rd ECM, Barcelona, July 10-14, 2000. Sections 2.2, 3.3, 3.4 changed, 2.3 removed to correct consequences of a miscalculation, a reference ...
Oleg Viro
semanticscholar +5 more sources
Algebraic Cycles and Approximation Theorems in Real Algebraic Geometry [PDF]
Transactions of the American Mathematical Society, 1993 Let \(M\) be a compact orientable smooth manifold of dimension \(\geq 5\). This paper shows which subgroups \(G \subset H_ 2 (M, {\mathbf Z}/2)\) can possibly be the subgroup of two dimensional algebraic cycles in an algebraic model of \(M\). It shows that the possible \(G\)'s are exactly those containing the Poincaré dual of the second Stieffel ...
J. Bochnak, Wojciech Kucharz
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Algebraically special, real alpha-geometries [PDF]
Journal of Geometry and Physics, 2011 We exploit the spinor description of four-dimensional Walker geometry, and conformal rescalings of such, to describe the local geometry of four-dimensional neutral geometries with algebraically degenerate self-dual Weyl curvature and an integrable distribution of alpha-planes (algebraically special real alpha-geometry).
Peter R. Law, Yasuo Matsushita
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On the geometry underlying a real Lie algebra representation [PDF]
Geometric, Algebraic and Topological Methods for Quantum Field Theory, 2012 Let $G$ be a real Lie group with Lie algebra $\mathfrak g$. Given a unitary representation $ $ of $G$, one obtains by differentiation a representation $d $ of $\mathfrak g$ by unbounded, skew-adjoint operators. Representations of $\mathfrak g$ admitting such a description are called \emph{integrable,} and they can be geometrically seen as the action ...
Rodrigo Vargas Le-Bert
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Moduli spaces and algebraic cycles in real algebraic geometry [PDF]
, 2022 This thesis intends to make a contribution to the theories of algebraic cycles and moduli spaces over the real numbers. In the study of the subvarieties of a projective algebraic variety, smooth over the field of real numbers, the cycle class map between the Chow ring and the equivariant cohomology ring plays an important role.
Olivier de Gaay Fortman
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Formulating problems for real algebraic geometry [PDF]
, 2014 We discuss issues of problem formulation for algorithms in real algebraic geometry, focussing on quantifier elimination by cylindrical algebraic decomposition.
Matthew England
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