Type I degeneration of Kunev surfaces

Usui, Sampei

Théorie de Hodge - Luminy, Juin 1987, Astérisque, no. 179-180 (1989), pp. 185-243.

Zbl

@incollection{AST_1989__179-180__185_0,
     author = {Usui, Sampei},
     title = {Type {I} degeneration of {Kunev} surfaces},
     booktitle = {Th\'eorie de Hodge - Luminy, Juin 1987},
     editor = {Barlet D. and Esnault H. and Elzein F. and Verdier Jean-Louis and Viehweg E.},
     series = {Ast\'erisque},
     pages = {185--243},
     publisher = {Soci\'et\'e math\'ematique de France},
     number = {179-180},
     year = {1989},
     zbl = {0755.14011},
     language = {en},
     url = {http://archive.numdam.org/item/AST_1989__179-180__185_0/}
}

TY  - CHAP
AU  - Usui, Sampei
TI  - Type I degeneration of Kunev surfaces
BT  - Théorie de Hodge - Luminy, Juin 1987
AU  - Collectif
ED  - Barlet D.
ED  - Esnault H.
ED  - Elzein F.
ED  - Verdier Jean-Louis
ED  - Viehweg E.
T3  - Astérisque
PY  - 1989
SP  - 185
EP  - 243
IS  - 179-180
PB  - Société mathématique de France
UR  - http://archive.numdam.org/item/AST_1989__179-180__185_0/
LA  - en
ID  - AST_1989__179-180__185_0
ER  -

%0 Book Section
%A Usui, Sampei
%T Type I degeneration of Kunev surfaces
%B Théorie de Hodge - Luminy, Juin 1987
%A Collectif
%E Barlet D.
%E Esnault H.
%E Elzein F.
%E Verdier Jean-Louis
%E Viehweg E.
%S Astérisque
%D 1989
%P 185-243
%N 179-180
%I Société mathématique de France
%U http://archive.numdam.org/item/AST_1989__179-180__185_0/
%G en
%F AST_1989__179-180__185_0

Usui, Sampei. Type I degeneration of Kunev surfaces, dans Théorie de Hodge - Luminy, Juin 1987, Astérisque, no. 179-180 (1989), pp. 185-243. http://archive.numdam.org/item/AST_1989__179-180__185_0/

Bibliographie
Cité par

[BPV] Barth, W., Peters, C. & Van De Ven, A., Compact complex surfaces, Springer-Verlag (1984). | DOI | Zbl

[Ca.1] Catanese, F., Surfaces with $K^{2} = p_{g} = 1$ and their period mapping, Proc. Summer Meeting, Copenhagen 1978, Lect. Notes in Math. No 732, Springer-Verlag (1979) pp.1-29. | Zbl

[Ca.2] Catanese, F., The moduli and the global period mapping of the surfaces with $K^{2} = p_{g} = 1$ : a counter-example to the global Torelli problem, Comp. Math. 41-3 (1980) 401-414. | EuDML | Numdam | Zbl

[C1.1] Clemens, C. H., Degenerations of Kahler manifolds, Duke Math. J. 44 (1977) 215-290. | DOI | Zbl

[C1.2] Clemens, C. H., A scrapbook of complex curve theory, Plenum Press (1980). | Zbl

[D] Deligne, P., Theorie de Hodge III, Publ. Math. IHES 44 (1974) 5-77. | DOI | EuDML | Numdam | Zbl

[GS] Griffiths, P. & Schmid, W., Recent develpments in Hodge theory: a discussion of techniques and results, Diecrete subgroups of Lie groups, Bombay, 1973, Oxford Univ. Press (1975) pp.31-127. | Zbl

[H.1] Horikawa, E., On deformations of quintic surfaces, Invent. Math. 31 (1975) 43-85. | DOI | EuDML | Zbl

[H.2] Horikawa, E., Surjectivity of period map of $K 3$ surfaces of degree $2$ , Math. Ann. 228 (1977) 113-146. | DOI | EuDML | Zbl

[Ko.1] Kodaira, K., On compact analytic surfaces II, Ann. of Math. 77 (1963) 563-626. | DOI | Zbl

[Ko.2] Kodaira, K., On the structure of compact complex analytic surfaces I, Amer. J. Math. 86 (1964) 751-798. | DOI | Zbl

[Ko.3] Kodaira, K., On homotopy $K 3$ surfaces, essays on topology and related topics, Mémoires dédiés à George de Rham, Springer-Verlag (1970) pp. 58-69. | Zbl

[Ku] Kulikov, V., Degenerations of $K 3$ surfaces and Enriques surfaces, Math. USSR Izvestija 11 (1977) 957-989. | DOI | Zbl

[L] Letizia, M., Intersections of a plane curve with a moving line and a generic global Torelli-type theorem for Kunev surfaces, Amer. J. Math. 106-5 (1984) 1135-1146. | DOI | Zbl

[Mi] Milnor, J., On simply connected $4$ -manifolds, Symp. Internac. de Topologia Algebrica, Univ. de Mexico, 1958. | Zbl

[Mo.1] Morrison, D., The CIemens-Schmid exact sequence and applications, Topics in transcendental algebraic geometry, ed. P. Griffiths, Ann. of Math. Studies 106, Princeton Univ. Press (1984) pp.101-120. | Zbl

[Mo.2] Morrison, D., On the moduli of Todorov surfaces, Algebraic Geometry and Commutative Algebra in Honor of Masayoshi Nagata ed. H. Hironaka et al., Kinokuniya C. LTD (1987) pp. 313-355. | Zbl

[Mu] Mumford, D., Semi-stable reduction, Toroidal Embeddings I, Lect. Notes in Math. No 339 (1973) pp. 53-108.

[P] Persson, U., Degeneration of algebraic surfaces, Mem. A.M.S. 189 (1977). | Zbl

[PP] Persson, U. & Pinkham, H., Degenerations of surfaces with trivial canonical bundle, Ann. of Math. 113 (1981) 45-66. | DOI | Zbl

[Sa.K] Saito, K., Einfach-elliptische Singularitäten, Invent. Math. 23 (1974) 289-325. | DOI | EuDML | Zbl

[Sa.M] Saito, M.-H., On the infinitesimal Torelli problem of elliptic surfaces, J. Math. Kyoto Univ. 23-3 (1983) 441-460. | DOI | Zbl

[Sc] Schmid, W., Variation of Hodge structure: the singularities of the period mappings, Invent. Math. 22 (1973) 211-320. | DOI | EuDML | Zbl

[Se] Seiler, W. K., Quotentenproblerne in der Invariantentheorie, Diplomarbeit 1977, Univ. Karlsruhe.

[Sh] Shah, J., A complete moduli space for $K 3$ surfaces of degree $2$ , Ann. of Math. 112 (1980) 485-510. | DOI | Zbl

[SSU] Saito, M.-H., Shimizu, Y. & Usui, S., Variation of mixed Hodge structure and Torelli problem, Algebraic Geometry, Sendai, 1985, Advanced Study of Pure Math. 10, North-Holland Publ. C. & Kinokuniya C LTD (1987) pp. 649-693. | DOI | Zbl

[T.1] Todorov, A. N., Surfaces of general type with $p_{g} = 1$ and $(K, K) = 1$ : I, Ann. scient. Ec. Norm. Sup. 4-13 (1980) 1-21. | EuDML | Numdam | Zbl

[T.2] Todorov, A. N., A construction of surfaces with $p_{g} = 1, q = 0$ and $2 \leq (K^{2}) \leq 8$ : Counterexamples of the global Torelli theorem, Invent. Math. 63 (1981) 287-304. | EuDML | Zbl

[Ue] Ueno, K., Kodaira dimensions for certain fibre spaces, Complex Analysis and Algebraic Geometry, A collection of papers dedicated to K. Kodaira, ed. W. L. Baily & T. Shioda, Iwanami-Shoten (1977) pp. 279-292. | Zbl

[Us.1] Usui, S., Period map of surfaces with $p_{g} = c \overset{2}{1} = 1$ and $K$ ample, Mem. Fac. Sci. Kochi Univ. (Math.) 3 (1981) 37-73. | Zbl

[Us.2] Usui, S., Effect of automorphisms on variation of Hodge structure, J. Math. Kyoto Univ. 21-4 (1981) 645-672. | DOI | Zbl

[Us.3] Usui, S., Variation of mixed Hodge structure arising from family of logarithmic deformations, Ann. scient. Éc. Norm. Sup. 4-16 (1983) 91-107. | DOI | EuDML | Numdam | Zbl

Usui, S., Variation of mixed Hodge structure arising from family of logarithmic deformations II: Classifying space, Duke Math. J. 51-4 1984 851-875. | DOI | Zbl

[Us.4] Usui, S., Degeneration of Kunev surfaces I; Proc. Japan Acad. 63-A-4 (1987) 110-113. | DOI | Zbl

Usui, S., Degeneration of Kunev surfaces II, Proc. Japan Acad. 63-A-4 (1987) 167-169. | DOI | Zbl

[Us.5] Usui, S., Examples of semi-stable degenerations of Kunev surfaces, Proc. Algebraic Geometry Seminar, Singapore, 1987, ed. M. Nagata & T. A. Peng, World Scientific (1988) pp. 115-139.