On the rationality of the period mapping
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Série 4, Tome 5 (1978) no. 4, pp. 683-717.
@article{ASNSP_1978_4_5_4_683_0,
     author = {Sommese, Andrew John},
     title = {On the rationality of the period mapping},
     journal = {Annali della Scuola Normale Superiore di Pisa - Classe di Scienze},
     pages = {683--717},
     publisher = {Scuola normale superiore},
     volume = {Ser. 4, 5},
     number = {4},
     year = {1978},
     zbl = {0396.32004},
     mrnumber = {519890},
     language = {en},
     url = {http://www.numdam.org/item/ASNSP_1978_4_5_4_683_0/}
}
Sommese, Andrew John. On the rationality of the period mapping. Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Série 4, Tome 5 (1978) no. 4, pp. 683-717. http://www.numdam.org/item/ASNSP_1978_4_5_4_683_0/

[1] A. Andreotti - F. Norguet, La convexité holomorphe dans l'espace analytique des cycles d'une variété algébrique, Ann. Scuola Norm. Sup. Pisa, 21 (1967), pp. 31-82. | Numdam | MR 239118 | Zbl 0176.04001

[2] A. Andreotti - W. Stoll, Analytic and algebraic dependence of meromorphic functions, Lecture Notes in Mathematics 234, Berlin - Heidelberg - New York, Springer, 1971. | MR 390298 | Zbl 0222.32013

[3] A. Andreotti - E. Vesentini, Carleman estimates for the Laplace-Beltrami operator on complex manifolds, Publ. Math. 25, I.H.E.S. (1965), pp. 81-130. | Numdam | MR 175148 | Zbl 0138.06604

[4] A. Andreotti - E. Vesentini, Sopra un Teorema di Kodaira, Ann. Scuola Norm. Sup. Pisa, 15 (1961), pp. 283-309. | Numdam | MR 141140 | Zbl 0108.16604

[5] D. Barlet, Espace analytique réduit des cycles analytiques complexes compacts d'un espace analytique complexe de dimension finie, Séminaire François Norguet 1974-1975, Lecture Notes in Mathematics 482, Berlin - Heidelberg - New York, Springer, 1975. | MR 399503 | Zbl 0331.32008

[6] A. Borel, Introduction aux groupes arithmétiques, Paris, Hermann, 1969. | MR 244260 | Zbl 0186.33202

[7] A. Borel, Some metric properties of arithmetic quotients of symmetric spaces and an extension theorem, J. Differential Geometry, 6 (1972), pp. 543-560. | MR 338456 | Zbl 0249.32018

[8] P. Deligne, Equations différentielles à points singuliers réguliers, Lecture Notes in Mathematics 163, Berlin - Heidelberg - New York, Springer, 1970. | MR 417174 | Zbl 0244.14004

[9] H. Grauert - O. Riemenschneider, Verschwindungssätze für analytisches Kohomologiegruppen auf komplexen Räumen, Invent. Math., 11 (1970), pp. 263-292. | MR 302938 | Zbl 0202.07602

[10] P. Griffiths, Periods of integrals on algebraic manifolds I, II, Amer. J. Math., 90 (1968), pp. 568-626, 805-865; III, Publ. Math. 38, I.H.E.S. (1970), pp. 125-180.

[11] P. Griffiths, Periods of integrals on algebraic manifolds, Bull. Amer. Math. Soc., 75 (1970), pp. 228-296. | MR 258824 | Zbl 0214.19802

[12] P. Griffiths - W. Schmid, Locally homogeneous complex manifolds, Acta Math., 123 (1970), pp. 253-302. | MR 259958 | Zbl 0209.25701

[13] P. Griffiths - W. Schmid, Recent developments in Hodge theory: a discussion of techniques and results, Bombay: Proc. Tata Inst. Conf. on Discrete Groups and Moduli, 1973. | Zbl 0355.14003

[14] P. Griffiths, Variations on a theorem of Abel, Invent. Math., 35 (1976), pp. 321-390. | MR 435074 | Zbl 0339.14003

[15] J.P. Henry - Le Dung Tráng, Limites d'espaces tangents, Séminaire François Norguet, Jan. 1974 - June 1975, Lecture Notes in Mathematics 482, Berlin- Heidelberg - New York, Springer (1975), pp. 251-265. | MR 393554 | Zbl 0319.32019

[16] H. Hironaka, Flattening theorem in complex-analytic geometry, Amer. J. Math., 97 (1976), pp. 503-547. | MR 393556 | Zbl 0307.32011

[17] H. Hironaka, Bimeromorphic smoothing of a complex-analytic space (Summary), Math. Inst. Warwick University, England, 1971.

[18] K. Kodaira, On Kähler varieties of restricted type, Ann. of Math., 60 (1954), pp. 28-48. | MR 68871 | Zbl 0057.14102

[19] R. Narasimhan, The Levi Problem for complex spaces, Math. Ann., 142 (1961), pp. 355-365. | MR 148943 | Zbl 0106.28603

[20] C. Peters, The local Torelli problem, I, Math. Ann., 217 (1975), pp. 1-16. | MR 441966 | Zbl 0293.14004

[21] R. Remmert, Holomorphe und meromorphe Abbildungen komplexer Räume, Math. Ann., 133 (1957), pp. 328-370. | MR 92996 | Zbl 0079.10201

[22] O. Riemenschneider, Characterizing Moisezon spaces by almost positive coherent sheaves, Math. Z. (1971), pp. 263-284. | MR 294714 | Zbl 0214.48501

[23] H. Rossi, Picard variety of an isolated singular point, Rice Univ. Studies, 54 (1968), pp. 63-73. | MR 244517 | Zbl 0179.40103

[24] W. Schmid, Variation of Hodge structures: the singularities of the period mapping, Invent. Math., 22 (1973), pp. 211-319. | MR 382272 | Zbl 0278.14003

[25] J.P. Serre, Géométrie algébrique et géométrie analytique, Ann. Inst. Fourier, Grenoble, 6 (1955), pp. 1-42. | Numdam | MR 82175 | Zbl 0075.30401

[26] B. Shiffman, Extension of positive line bundles and meromorphic maps, Invent. Math., 15 (1972), pp. 332-347. | MR 374489 | Zbl 0223.32017

[27] Y.-T. Siu, Analyticity of sets associated to Lelong numbers and the extension of closed positive currents, Invent. Math., 27 (1974), pp. 53-126. | MR 352516 | Zbl 0289.32003

[28] A. Sommese, Algebraic properties of the period mapping, Princeton University Thesis, June 1973.

[29] A. Sommese, Criteria for quasi -projectivity, Math. Ann., 217 (1975), pp. 247-256. | MR 385177 | Zbl 0338.14011

[30] A. Sommese, Addendum to « Criteria for quasi-projectivity », Math. Ann., 221 (1976), pp. 95-96. | MR 402129 | Zbl 0338.14012

[31] A. Weil, Sur les théorèmes de de Rham, Comment. Math. Helv., 26 (1952), pp. 119-145. | MR 50280 | Zbl 0047.16702

[32] H. Whitney, Tangents to an analytic variety, Ann. of Math., 81 (1965), pp. 496-549. | MR 192520 | Zbl 0152.27701