Relative topology of real algebraic varieties in their complexifications [PDF]
Pacific Journal of Mathematics, 2004 An algebraic model of a closed smooth manifold \(M\) is a nonsingular real algebraic variety \(X\) diffeomorphic to \(M\) (such a model always exists). In this paper, the existence of such models \(X\) having good complexifications is considered. The main result states that \(M\) is formal (in the sense of Sullivan) if it admits an algebraic model \(X\)
Yildiray Ozan
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The topology of Real Algebraic Varieties [PDF]
Current Developments in Mathematics, 2000 János Kollár
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Sampling Real Algebraic Varieties for Topological Data Analysis [PDF]
2019 18th IEEE International Conference On Machine Learning And Applications (ICMLA), 2019 Topological data analysis (TDA) provides a growing body of tools for computing geometric and topological information about spaces from a finite sample of points. We present a new adaptive algorithm for finding provably dense samples of points on real algebraic varieties given a set of defining polynomials.
Emilie Dufresne +3 more
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Semialgebraic topology over a real closed field I: Paths and components in the set of rational points of an algebraic variety [PDF]
Mathematische Zeitschrift, 1981 We fix once and for all a real closed base field R. By a variety X over R we mean a separated algebraic scheme X over R. For all problems attacked here we could equally well assume that X is also reduced, since we are only interested in the set X(R) of rational points of X.
KNEBUSCH, Manfred, Delfs, Hans
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Topological properties of real algebraic varieties: du coté de chez Rokhlin [PDF]
Russian Mathematical Surveys, 2000 The survey gives an overview of the achievements in topology of real algebraic varieties in the direction initiated in the early 70th by V.I.Arnold and V.A.Rokhlin. We make an attempt to systematize the principal results in the subject. After an exposition of general tools and results, special attention is paid to surfaces and curves on surfaces.
Degtyarev, A. I., Kharlamov, V. M.
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Explicit estimates for Betti numbers and their arithmetic applications
四川大学学报. 自然科学版This survey discusses explicit estimates for Betti numbers of algebraic varieties and their arith-metic applications.The guiding problem is to bound the total Betti number， or the compactly supported total Betti number， of a variety defined by equations ...
WAN Daqing, ZHANG Dingxin
doaj
A topological characterization of real algebraic varieties [PDF]
Bulletin of the American Mathematical Society, 1980 Akbulut, Selman, King, Henry C.
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Topological properties of real algebraic varieties: Rokhlin's way.
, 1999 This is a survey which gives an overview of the achievements in topology of real algebraic varieties initiated in the early 70th by V.I.Arnold and V.A.Rokhlin. We make an attempt to systematize the principal results in the subject. After an exposition of general tools and results, special attention is paid to surfaces and curves on surfaces.
Degtyarev, Alexander +1 more
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DNA Sequence and Structure under the Prism of Group Theory and Algebraic Surfaces. [PDF]
Int J Mol Sci, 2022 Planat M +5 more
europepmc +1 more source
The space of homogeneous probability measures on Γ\X¯maxS is compact: With an appendix by Jialun Li. [PDF]
Math Ann, 2023 Daw C, Gorodnik A, Ullmo E.
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