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On the subvarieties with nonsingular real loci of a real algebraic variety

Olivier Benoist

Geometry & Topology 28 (2024) 1693–1725
Bibliography
1 R Abraham, J Robbin, Transversal mappings and flows, Benjamin (1967) MR0240836
2 J F Adams, Stable homotopy and generalised homology, Univ. Chicago Press (1974) MR0402720
3 S Akbulut, H C King, Real algebraic structures on topological spaces, Publ. Math. Inst. Hautes Études Sci. 53 (1981) 79 MR0623536
4 S Akbulut, H King, Submanifolds and homology of nonsingular real algebraic varieties, Amer. J. Math. 107 (1985) 45 MR0778089
5 S Akbulut, H King, Polynomial equations of immersed surfaces, Pacific J. Math. 131 (1988) 209 MR0922214
6 S Akbulut, H King, Topology of real algebraic sets, 25, Springer (1992) MR1225577
7 S Akbulut, H King, Transcendental submanifolds of ℝℙn, Comment. Math. Helv. 80 (2005) 427 MR2142249
8 A Andreotti, T Frankel, The Lefschetz theorem on hyperplane sections, Ann. of Math. 69 (1959) 713 MR0177422
9 A Beauville, Quelques remarques sur la transformation de Fourier dans l’anneau de Chow d’une variété abélienne, from: "Algebraic geometry" (editors M Raynaud, T Shioda), Lecture Notes in Math. 1016, Springer (1983) 238 MR0726428
10 R Benedetti, A Tognoli, Approximation theorems in real algebraic geometry, Boll. Un. Mat. Ital. Suppl. 1980 (1980) 209 MR0675502
11 R Benedetti, A Tognoli, On real algebraic vector bundles, Bull. Sci. Math. 104 (1980) 89 MR0560747
12 O Benoist, O Debarre, Smooth subvarieties of Jacobians, Épijournal Géom. Algébrique (2023) 2 MR4671731
13 O Benoist, O Wittenberg, On the integral Hodge conjecture for real varieties, I, Invent. Math. 222 (2020) 1 MR4145787
14 O Benoist, O Wittenberg, On the integral Hodge conjecture for real varieties, II, J. Éc. Polytech. Math. 7 (2020) 373 MR4077580
15 C Birkenhake, H Lange, Complex abelian varieties, 302, Springer (2004) MR2062673
16 J Bochnak, M Coste, M F Roy, Real algebraic geometry, 36, Springer (1998) MR1659509
17 J Bochnak, W Kucharz, On approximation of smooth submanifolds by nonsingular real algebraic subvarieties, Ann. Sci. École Norm. Sup. 36 (2003) 685 MR2032984
18 A Borel, A Haefliger, La classe d’homologie fondamentale d’un espace analytique, Bull. Soc. Math. France 89 (1961) 461 MR0149503
19 L Bröcker, Reelle Divisoren, Arch. Math. (Basel) 35 (1980) 140 MR0578031
20 J L Colliot-Thélène, F Ischebeck, L’équivalence rationnelle sur les cycles de dimension zéro des variétés algébriques réelles, C. R. Acad. Sci. Paris Sér. I Math. 292 (1981) 723 MR0618896
21 P E Conner, Differentiable periodic maps, 738, Springer (1979) MR0548463
22 V Cossart, O Piltant, Resolution of singularities of threefolds in positive characteristic, II, J. Algebra 321 (2009) 1836 MR2494751
23 M Coste, M Shiota, Nash triviality in families of Nash manifolds, Invent. Math. 108 (1992) 349 MR1161096
24 O Debarre, Sous-variétés de codimension 2 d’une variété abélienne, C. R. Acad. Sci. Paris Sér. I Math. 321 (1995) 1237 MR1360790
25 H Delfs, M Knebusch, Semialgebraic topology over a real closed field, II : Basic theory of semialgebraic spaces, Math. Z. 178 (1981) 175 MR0631628
26 W Fulton, Intersection theory, 2, Springer (1984) MR732620
27 A Grothendieck, Éléments de géométrie algébrique, IV : Étude locale des schémas et des morphismes de schémas, II, Publ. Math. Inst. Hautes Études Sci. 24 (1965) 5 MR0199181
28 A Grothendieck, Éléments de géométrie algébrique, IV : Étude locale des schémas et des morphismes de schémas, III, Publ. Math. Inst. Hautes Études Sci. 28 (1966) 5 MR0217086
29 R Hartshorne, Algebraic geometry, 52, Springer (1977) MR0463157
30 R Hartshorne, E Rees, E Thomas, Nonsmoothing of algebraic cycles on Grassmann varieties, Bull. Amer. Math. Soc. 80 (1974) 847 MR0357402
31 H Hironaka, Smoothing of algebraic cycles of small dimensions, Amer. J. Math. 90 (1968) 1 MR0224611
32 M W Hirsch, Differential topology, 33, Springer (1976) MR448362
33 C Huneke, B Ulrich, Divisor class groups and deformations, Amer. J. Math. 107 (1985) 1265 MR0815763
34 C Huneke, B Ulrich, The structure of linkage, Ann. of Math. 126 (1987) 277 MR0908149
35 C Huneke, B Ulrich, Algebraic linkage, Duke Math. J. 56 (1988) 415 MR0948528
36 F Ischebeck, H W Schülting, Rational and homological equivalence for real cycles, Invent. Math. 94 (1988) 307 MR0958834
37 S L Kleiman, Geometry on Grassmannians and applications to splitting bundles and smoothing cycles, Publ. Math. Inst. Hautes Études Sci. 36 (1969) 281 MR0265371
38 S O Kochman, Bordism, stable homotopy and Adams spectral sequences, 7, Amer. Math. Soc. (1996) MR1407034
39 V A Krasnov, Characteristic classes of vector bundles on a real algebraic variety, Izv. Akad. Nauk SSSR Ser. Mat. 55 (1991) 716 MR1137584
40 V A Krasnov, On the equivariant Grothendieck cohomology of a real algebraic variety and its application, Izv. Ross. Akad. Nauk Ser. Mat. 58 (1994) 36 MR1286838
41 W Kucharz, Rational and homological equivalence of real algebraic cycles, Geom. Dedicata 106 (2004) 113 MR2079837
42 W Kucharz, Transcendental submanifolds of projective space, Comment. Math. Helv. 84 (2009) 127 MR2466077
43 W Kucharz, J van Hamel, Transcendental manifolds in real projective space and Stiefel–Whitney classes, Ann. Sc. Norm. Super. Pisa Cl. Sci. 8 (2009) 267 MR2548247
44 D Laksov, Residual intersections and Todd’s formula for the double locus of a morphism, Acta Math. 140 (1978) 75 MR0466137
45 K Lamotke, The topology of complex projective varieties after S Lefschetz, Topology 20 (1981) 15 MR0592569
46 P W Michor, Manifolds of differentiable mappings, 3, Shiva (1980) MR0583436
47 J Milnor, On the cobordism ring Ω and a complex analogue, I, Amer. J. Math. 82 (1960) 505 MR0119209
48 J Milnor, On the Stiefel–Whitney numbers of complex manifolds and of spin manifolds, Topology 3 (1965) 223 MR0180977
49 J W Milnor, J D Stasheff, Characteristic classes, 76, Princeton Univ. Press (1974) MR0440554
50 V K Murty, Exceptional Hodge classes on certain abelian varieties, Math. Ann. 268 (1984) 197 MR0744607
51 C Peskine, L Szpiro, Liaison des variétés algébriques, I, Invent. Math. 26 (1974) 271 MR0364271
52 D Quillen, Elementary proofs of some results of cobordism theory using Steenrod operations, Adv. Math. 7 (1971) 29 MR0290382
53 E Rees, E Thomas, On the divisibility of certain Chern numbers, Q. J. Math. 28 (1977) 389 MR0467771
54 E Rees, E Thomas, Realizing homology classes by almost-complex submanifolds, Math. Z. 172 (1980) 195 MR0580860
55 A M Robert, A course in p–adic analysis, 198, Springer (2000) MR1760253
56 C Scheiderer, Purity theorems for real spectra and applications, from: "Real analytic and algebraic geometry" (editors F Broglia, M Galbiati, A Tognoli), de Gruyter (1995) 229 MR1320322
57 M Seppälä, R Silhol, Moduli spaces for real algebraic curves and real abelian varieties, Math. Z. 201 (1989) 151 MR0997218
58 R Thom, Quelques propriétés globales des variétés différentiables, Comment. Math. Helv. 28 (1954) 17 MR0061823
59 J A Todd, Invariant and covariant systems on an algebraic variety, Proc. Lond. Math. Soc. 46 (1940) 199 MR0002214
60 C T C Wall, Differential topology, 156, Cambridge Univ. Press (2016) MR3558600
61 H Whitney, Differentiable manifolds, Ann. of Math. 37 (1936) 645 MR1503303
62 H Whitney, The self-intersections of a smooth n–manifold in 2n–space, Ann. of Math. 45 (1944) 220 MR0010274