Arc spaces and additive invariants in real algebraic and analytic geometry

Arc spaces and additive invariants in real algebraic and analytic geometry Download PDF EPUB FB2

Generally, real algebraic geometry uses methods of its own that usually differ sharply from the more widely known methods of complex algebraic geometry. This feature is particularly apparent when studying the basic topological and geometric properties of real algebraic sets; the rich algebraic structures are usually hidden and cannot be recovered from the topology.

The use of arc spaces and additive invariants. Stanford Libraries' official online search tool for books, media, journals, databases, government documents and more.

Arc spaces and additive invariants in real algebraic and analytic geometry. Panoramas and Syntheses vol By Krzysztof Kurdyka, Toshizumi Fukui, Adam Parusinski, Laurentiu Paunescu, Michel Coste and Clint Mccrory.

Finally, as an application, we characterize in terms of the motivic measure, germs of arc-analytic homeomorphism between real algebraic varieties which are bi-Lipschitz for the inner metric.

We investigate connections between Lipschitz geometry of real algebraic varieties and properties of their arc : Jean-Baptiste Campesato, Toshizumi Fukui, Krzysztof Kurdyka, Adam Parusiński.

Title: Geometry on arc spaces of algebraic varieties. Abstract: This paper is a survey on arc spaces, a recent topic in algebraic geometry and singularity theory. The geometry of the arc space of an algebraic variety yields several new geometric invariants and brings new light to some classical by:   Kurdyka, K., Parusiński, A.: Arc-symmetric sets and arc-analytic mappings in Arc spaces and additive invariants in real algebraic and analytic geometry.

Panor. Synthèses. Soc. Math. 24, 33–67 () MATH; Google ScholarCited by: 5. Fukui and L. Paunescu, On blow-analytic equivalence, to appear In: Arc Spaces and Additive Invariants in Real Algebraic Geometry, Proceedings of Winter School, Real algebraic and Analytic Geometry and Motivic Integration, Aussois,(eds.

Coste, K. Kurdyka and A. Parusinski), Panoramas et Synthèses, by: 3. Jan Denef and Franc¸ois Loeser. Abstract. This paper is a survey on arc spaces, a recent topic in algebraic geometry and singularity theory.

The geometry of the arc space of an algebraic variety yields several new geometric invariants and brings new light to some classical invariants. Toshizumi Fukui's research while affiliated with invariants in real algebraic and analytic geometry.

Panoramas and Syntheses vol geometry based on the study of arc spaces and additive. In this paper we show that the non-analyticity locus of an arc-analytic function is arc-symmetric. Recall that a function is called arc-analytic if it is real analytic on each real analytic arc. Arc-symmetric Sets and Arc-analytic Mappings, (with K.

Kurdyka), course at Winter School Real Algebraic and Analytic Geometry and Motivic Integration, Aussois, Savoie, in "Arcs Spaces and Additive Invariants in Real algebraic and Analytic Geometry", Panoramas et Synthèses, 24.

Arc spaces and additive invariants in real algebraic and analytic geometry. Paris: Société Mathématique de France ; Providence, RI: AMS [distributor], © (OCoLC) Material Type: Internet resource: Document Type: Book, Internet Resource: All Authors / Contributors: M Coste.

Fukui and L. Paunescu, On blow-analytic equivalence, In: Arc Spaces and Additive Invariants in Real Algebraic Geometry, Proceedings of Winter School “Real algebraic and Analytic Geometry and Motivic Integration”, Aussoisby: 8.

Get this from a library. Arc spaces and additive invariants in real algebraic and analytic geometry. [; et al]. Arc spaces, motivic measure and Lipschitz property of real algebraic varieties, Math Ann, Feb (old version) T. Fukui Local differential geometry of cuspidal edge and swallowtail, preprint T.

Arc geometry and algebra: foliations, moduli spaces, string topology and field theory Ralph M. Kaufmann Contents [41], [3], [40]. This theory was originally introduced in algebraic topology to study loop spaces, but has had a renaissance in conjunction with the deepening interaction Arc geometry and algebra of two variable real analytic function germs, J.

of Algebraic Geometry 19 (), —] and only partial results for n > 2. The latter are based on 'motivic typo invariants" introduced in [S. Koike and A. Parusiúski, Motivic- type invariants of blow-analytic equivalence Ann. Inst. Fourier 53 (). Coste, et al. (Eds.), Arc Spaces and Additive Invariants in Real Algebraic and Analytic Geometry, Panoramas et Synthèses, vol.

24, Soc. Math. France (), pp. Author: Clint McCrory, Adam Parusiński. Our main object of interest here are the so called arc-analytic functions. A function f: S!R on a set SˆRn is said to be arc-analytic when f is analytic for every real analytic arc: (";")!S. Arc-analytic functions, although relatively unknown among non-specialists, play an important role in modern real algebraic and analytic geometry (see.

These lecture notes have been prepared for the Summer school on ”Moduli spaces and arcs in algebraic geometry”, Cologne, August The goal is to explain the rele-vance of spaces of arcs to birational geometry.

In the first section we introduce the spaces of arcs and their finite-dimensional approximations, the spaces of jets. In the. adshelp[at] The ADS is operated by the Smithsonian Astrophysical Observatory under NASA Cooperative Agreement NNX16AC86A.Enumerative Invariants in Algebraic Geometry and String Theory: Lectures given at the C.I.M.E.

Summer School held in Cetraro, Italy, June(Lecture Notes in Mathematics) th Edition by Dan Abramovich (Author), Marcos Mariño (Contributor), Michael Thaddeus (Contributor), Ravi Vakil (Contributor) & 1 moreAuthor: Marcos Marino.Arc-symmetric sets and arc-analytic functions were introduced by the first-named author.

One of the motivation was a striking difference between real algebraic (or analytic) geometry and the geometry over the field of complex numbers or more generally over an algebraically closed field. In the complex case the topology is adquate to the algebra; for instance the irreducible sets are connected Cited by: