Volume 20, issue 1 (2016)

Download this article
Download this article For screen
For printing
Recent Issues

Volume 23
Issue 5, 2165–2700
Issue 4, 1621–2164
Issue 3, 1085–1619
Issue 2, 541–1084
Issue 1, 1–540

Volume 22, 7 issues

Volume 21, 6 issues

Volume 20, 6 issues

Volume 19, 6 issues

Volume 18, 5 issues

Volume 17, 5 issues

Volume 16, 4 issues

Volume 15, 4 issues

Volume 14, 5 issues

Volume 13, 5 issues

Volume 12, 5 issues

Volume 11, 4 issues

Volume 10, 4 issues

Volume 9, 4 issues

Volume 8, 3 issues

Volume 7, 2 issues

Volume 6, 2 issues

Volume 5, 2 issues

Volume 4, 1 issue

Volume 3, 1 issue

Volume 2, 1 issue

Volume 1, 1 issue

The Journal
About the Journal
Editorial Board
Subscriptions
Editorial Interests
Editorial Procedure
Submission Guidelines
Submission Page
Ethics Statement
ISSN (electronic): 1364-0380
ISSN (print): 1465-3060
Author Index
To Appear
 
Other MSP Journals
On the Hodge conjecture for $q$–complete manifolds

Franc Forstnerič, Jaka Smrekar and Alexandre Sukhov

Geometry & Topology 20 (2016) 353–388
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 lim ←− 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