Geometry & Topology Volume 20, issue 1 (2016)

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On the Hodge conjecture for $q$–complete manifolds

Franc Forstnerič, Jaka Smrekar and Alexandre Sukhov

Geometry & Topology 20 (2016) 353–388

DOI: 10.2140/gt.2016.20.353

Bibliography

1	A Andreotti, T Frankel, The Lefschetz theorem on hyperplane sections, Ann. of Math. 69 (1959) 713 MR0177422
2	A Andreotti, R Narasimhan, A topological property of Runge pairs, Ann. of Math. 76 (1962) 499 MR0140714
3	A Andreotti, F Norguet, Cycles of algebraic manifolds and ∂∂–cohomology, Ann. Scuola Norm. Sup. Pisa 25 (1971) 59 MR0288314
4	M F Atiyah, F Hirzebruch, Vector bundles and homogeneous spaces, Proc. Sympos. Pure Math. 3, Amer. Math. Soc. (1961) 7 MR0139181
5	M F Atiyah, F Hirzebruch, Analytic cycles on complex manifolds, Topology 1 (1962) 25 MR0145560
6	E Ballico, F Catanese, C Ciliberto, editors, Classification of irregular varieties: minimal models and abelian varieties, 1515, Springer (1992) MR1180332
7	W Barth, Der Abstand von einer algebraischen Mannigfaltigkeit im komplex-projektiven Raum, Math. Ann. 187 (1970) 150 MR0268181
8	G E Bredon, Topology and geometry, 139, Springer (1993) MR1224675
9	V M Buhštaber, Modules of differentials of the Atiyah–Hirzebruch spectral sequence, II, Mat. Sb. 83 (1970) 61 MR0300284
10	M Colţoiu, q–convexity : a survey, from: "Complex analysis and geometry" (editors V Ancona, E Ballico, R M Mirò-Roig, A Silva), Pitman Res. Notes Math. Ser. 366, Longman, Harlow (1997) 83 MR1477441
11	M Cornalba, P Griffiths, Analytic cycles and vector bundles on non-compact algebraic varieties, Invent. Math. 28 (1975) 1 MR0367263
12	P Deligne, The Hodge conjecture, from: "The millennium prize problems" (editors J Carlson, A Jaffe, A Wiles), Clay Math. Inst. (2006) 45 MR2238273
13	J P Demailly, Cohomology of q–convex spaces in top degrees, Math. Z. 204 (1990) 283 MR1055992
14	J P Demailly, Analytic methods in algebraic geometry, 1, International Press (2012) MR2978333
15	S Donaldson, On the existence of symplectic submanifolds, from: "Contact and symplectic geometry" (editor C B Thomas), Publ. Newton Inst. 8, Cambridge Univ. Press (1996) 307 MR1432468
16	S K Donaldson, Symplectic submanifolds and almost-complex geometry, J. Differential Geom. 44 (1996) 666 MR1438190
17	A Dor, Immersions and embeddings in domains of holomorphy, Trans. Amer. Math. Soc. 347 (1995) 2813 MR1282885
18	A Douady, Cycles analytiques (d’après M F Atiyah et F Hirzebruch), from: "Séminaire Bourbaki 1961∕1962 (Exposé 223)", W. A. Benjamin (1966) MR1611206
19	B Drinovec Drnovšek, F Forstnerič, Holomorphic curves in complex spaces, Duke Math. J. 139 (2007) 203 MR2352132
20	B Drinovec-Drnovšek, F Forstnerič, Approximation of holomorphic mappings on strongly pseudoconvex domains, Forum Math. 20 (2008) 817 MR2445119
21	B Drinovec Drnovšek, F Forstnerič, Strongly pseudoconvex domains as subvarieties of complex manifolds, Amer. J. Math. 132 (2010) 331 MR2654777
22	O Forster, Plongements des variétés de Stein, Comment. Math. Helv. 45 (1970) 170 MR0269880
23	F Forstnerič, Noncritical holomorphic functions on Stein manifolds, Acta Math. 191 (2003) 143 MR2051397
24	F Forstnerič, Holomorphic flexibility properties of complex manifolds, Amer. J. Math. 128 (2006) 239 MR2197073
25	F Forstnerič, Stein manifolds and holomorphic mappings: the homotopy principle in complex analysis, 56, Springer (2011) MR2975791
26	F Forstnerič, J Globevnik, Discs in pseudoconvex domains, Comment. Math. Helv. 67 (1992) 129 MR1144617
27	H Grauert, Analytische Faserungen über holomorph-vollständigen Räumen, Math. Ann. 135 (1958) 263 MR0098199
28	H Grauert, On Levi’s problem and the imbedding of real-analytic manifolds, Ann. of Math. 68 (1958) 460 MR0098847
29	H Grauert, Une notion de dimension cohomologique dans la théorie des espaces complexes, Bull. Soc. Math. France 87 (1959) 341 MR1505124
30	H Grauert, Theory of q–convexity and q–concavity, from: "Several complex variables, VII" (editors H Grauert, T Peternell, R Remmert), Encyclopaedia Math. Sci. 74, Springer (1994) 259 MR1326623
31	M L Green, Infinitesimal methods in Hodge theory, from: "Algebraic cycles and Hodge theory" (editors A Albano, F Bardelli), Lecture Notes in Math. 1594, Springer, Berlin (1994) 1 MR1335239
32	P Griffiths, J Harris, On the Noether–Lefschetz theorem and some remarks on codimension-two cycles, Math. Ann. 271 (1985) 31 MR779603
33	A Grothendieck, Hodge’s general conjecture is false for trivial reasons, Topology 8 (1969) 299 MR0252404
34	H A Hamm, Zur Homotopietyp Steinscher Räume, J. Reine Angew. Math. 338 (1983) 121 MR684017
35	H A Hamm, Zum Homotopietyp q–vollständiger Räume, J. Reine Angew. Math. 364 (1986) 1 MR817633
36	G M Henkin, J Leiterer, Andreotti–Grauert theory by integral formulas, 74, Birkhäuser (1988) 270 MR986248
37	W V D Hodge, The topological invariants of algebraic varieties, from: "Proceedings of the International Congress of Mathematicians, I", Amer. Math. Soc. (1952) 182 MR0046075
38	C U Jensen, Les foncteurs dérivés de et leurs applications en théorie des modules, 254, Springer (1972) MR0407091
39	B Jöricke, Envelopes of holomorphy and holomorphic discs, Invent. Math. 178 (2009) 73 MR2534093
40	S Kaliman, M Zaĭdenberg, A tranversality theorem for holomorphic mappings and stability of Eisenman–Kobayashi measures, Trans. Amer. Math. Soc. 348 (1996) 661 MR1321580
41	K Kodaira, D C Spencer, Divisor class groups on algebraic varieties, Proc. Nat. Acad. Sci. USA 39 (1953) 872 MR0063122
42	W S Massey, Singular homology theory, 70, Springer (1980) MR569059
43	J Milnor, On axiomatic homology theory, Pacific J. Math. 12 (1962) 337 MR0159327
44	T Ohsawa, Completeness of noncompact analytic spaces, Publ. Res. Inst. Math. Sci. 20 (1984) 683 MR759689
45	M Peternell, q–completeness of subsets in complex projective space, Math. Z. 195 (1987) 443 MR895316
46	M Schneider, Über eine Vermutung von Hartshorne, Math. Ann. 201 (1973) 221 MR0357858
47	G Sorani, Omologia degli spazi q–pseudoconvessi, Ann. Scuola Norm. Sup. Pisa 16 (1962) 299 MR0157005
48	C Soulé, C Voisin, Torsion cohomology classes and algebraic cycles on complex projective manifolds, Adv. Math. 198 (2005) 107 MR2183252
49	E H Spanier, Algebraic topology, Springer (1981) MR666554
50	B Totaro, Torsion algebraic cycles and complex cobordism, J. Amer. Math. Soc. 10 (1997) 467 MR1423033
51	S Trivedi, Stratified transversality of holomorphic maps, Internat. J. Math. 24 (2013) 1350106, 12 MR3158578
52	C A Weibel, An introduction to homological algebra, 38, Cambridge Univ. Press (1994) MR1269324