Algebraic stratified general position and transversality
Authors:
Clint McCrory, Adam Parusiński and Laurenţiu Păunescu
Journal:
J. Algebraic Geom. 28 (2019), 139-152
DOI:
https://doi.org/10.1090/jag/713
Published electronically:
September 21, 2018
MathSciNet review:
3875363
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Abstract |
References |
Additional Information
Abstract: The method of Whitney interpolation is used to construct, for any real or complex projective algebraic variety, a stratified submersive family of self-maps that yields stratified general position and transversality theorems for semialgebraic subsets.
References
- Mark Goresky and Robert MacPherson, Intersection homology theory, Topology 19 (1980), no. 2, 135–162. MR 572580, DOI https://doi.org/10.1016/0040-9383%2880%2990003-8
- Mark Goresky and Robert MacPherson, Stratified Morse theory, Ergebnisse der Mathematik und ihrer Grenzgebiete (3) [Results in Mathematics and Related Areas (3)], vol. 14, Springer-Verlag, Berlin, 1988. MR 932724
- Clint McCrory, Stratified general position, Algebraic and geometric topology (Proc. Sympos., Univ. California, Santa Barbara, Calif., 1977) Lecture Notes in Math., vol. 664, Springer, Berlin, 1978, pp. 142–146. MR 518413
- Clint McCrory and Adam Parusiński, Real intersection homology, Topology Appl. 234 (2018), 108–129. MR 3739460, DOI https://doi.org/10.1016/j.topol.2017.07.018
- Claudio Murolo, A survey on stratified transversality, Singularity theory, World Sci. Publ., Hackensack, NJ, 2007, pp. 761–785. MR 2342939, DOI https://doi.org/10.1142/9789812707499_0033
- C. Murolo, D. J. A. Trotman, and A. A. du Plessis, Stratified transversality by isotopy, Trans. Amer. Math. Soc. 355 (2003), no. 12, 4881–4900. MR 1997589, DOI https://doi.org/10.1090/S0002-9947-03-03236-7
- Adam Parusiński and Laurenţiu Păunescu, Arc-wise analytic stratification, Whitney fibering conjecture and Zariski equisingularity, Adv. Math. 309 (2017), 254–305. MR 3607278, DOI https://doi.org/10.1016/j.aim.2017.01.016
- Hassler Whitney, Complex analytic varieties, Addison-Wesley Publishing Co., Reading, Mass.-London-Don Mills, Ont., 1972. MR 0387634
References
- Mark Goresky and Robert MacPherson, Intersection homology theory, Topology 19 (1980), no. 2, 135–162. MR 572580, DOI https://doi.org/10.1016/0040-9383%2880%2990003-8
- Mark Goresky and Robert MacPherson, Stratified Morse theory, Ergebnisse der Mathematik und ihrer Grenzgebiete (3) [Results in Mathematics and Related Areas (3)], vol. 14, Springer-Verlag, Berlin, 1988. MR 932724
- Clint McCrory, Stratified general position, Algebraic and geometric topology (Proc. Sympos., Univ. California, Santa Barbara, Calif., 1977) Lecture Notes in Math., vol. 664, Springer, Berlin, 1978, pp. 142–146. MR 518413
- Clint McCrory and Adam Parusiński, Real intersection homology, Topology Appl. 234 (2018), 108–129. MR 3739460, DOI https://doi.org/10.1016/j.topol.2017.07.018
- Claudio Murolo, A survey on stratified transversality, Singularity theory, World Sci. Publ., Hackensack, NJ, 2007, pp. 761–785. MR 2342939, DOI https://doi.org/10.1142/9789812707499_0033
- C. Murolo, D. J. A. Trotman, and A. A. du Plessis, Stratified transversality by isotopy, Trans. Amer. Math. Soc. 355 (2003), no. 12, 4881–4900. MR 1997589, DOI https://doi.org/10.1090/S0002-9947-03-03236-7
- Adam Parusiński and Laurenţiu Păunescu, Arc-wise analytic stratification, Whitney fibering conjecture and Zariski equisingularity, Adv. Math. 309 (2017), 254–305. MR 3607278, DOI https://doi.org/10.1016/j.aim.2017.01.016
- Hassler Whitney, Complex analytic varieties, Addison-Wesley Publishing Co., Reading, Mass.-London-Don Mills, Ont., 1972. MR 0387634
Additional Information
Clint McCrory
Affiliation:
Department of Mathematics, University of Georgia, Athens, Georgia 30602
MR Author ID:
122240
Email:
clint@math.uga.edu
Adam Parusiński
Affiliation:
Université Nice Sophia Antipolis, CNRS, LJAD, UMR 7351, 06108 Nice, France
Email:
adam.parusinski@unice.fr
Laurenţiu Păunescu
Affiliation:
School of Mathematics, University of Sydney, Sydney, NSW, 2006, Australia
Email:
laurent@maths.usyd.edu.au
Received by editor(s):
February 14, 2017
Received by editor(s) in revised form:
August 16, 2017, September 17, 2017, and October 26, 2017
Published electronically:
September 21, 2018
Additional Notes:
This work was partially supported by ANR project STAAVF (ANR-2011 BS01 009), by ARC DP150103113, by Sydney University BSG2014, and by Faculty of Science PSSP
Article copyright:
© Copyright 2018
University Press, Inc.
