Deformations of theta divisors and the rank 4 quadrics problem
Compositio Mathematica, Tome 76 (1990) no. 3, p. 367-398
@article{CM_1990__76_3_367_0,
     author = {Smith, Roy and Varley, Robert},
     title = {Deformations of theta divisors and the rank $4$ quadrics problem},
     journal = {Compositio Mathematica},
     publisher = {Kluwer Academic Publishers},
     volume = {76},
     number = {3},
     year = {1990},
     pages = {367-398},
     zbl = {0745.14012},
     mrnumber = {1080008},
     language = {en},
     url = {http://www.numdam.org/item/CM_1990__76_3_367_0}
}
Smith, Roy; Varley, Robert. Deformations of theta divisors and the rank $4$ quadrics problem. Compositio Mathematica, Tome 76 (1990) no. 3, pp. 367-398. http://www.numdam.org/item/CM_1990__76_3_367_0/

[A] M. Artin, Lectures on deformations of singularities, Tata Institute of Fundamental Research, Bombay, 1976. | Zbl 0395.14003

[A-H] E. Arbarello and J. Harris, Canonical curves and quadrics of rank 4, Comp. Math. 43 (1981), 145-179. | Numdam | MR 622446 | Zbl 0494.14011

[A-M] A. Andreotti and A. Mayer, On period relations for abelian integrals and algebraic curves, Ann. Scuola Norm. Sup. Pisa 21 (1967), 189-238. | Numdam | MR 220740 | Zbl 0222.14024

[B-V] F. Bardelli and L. Verdi, On osculating cones and the Riemann-Kempf singularity theorem for hyperelliptic curves, trigonal curves, and smooth plane quintics, Comp. Math. 65 (1988), 177-199. | Numdam | MR 932643 | Zbl 0662.14015

[C] C.H. Clemens, The local geometry of the Abel-Jacobi mapping, in Algebraic Geometry, Bowdoin 1985, Proceedings of Symposia in Pure Mathematics, A.M.S., vol. 46-part 2. | Zbl 0646.14020

[C-E] H. Cartan and S. Eilenberg, Homological Algebra, Princeton Univ. Press, 1956. | MR 77480 | Zbl 0075.24305

[Go] R. Godement, Topologie Algébrique et Théorie des Faisceaux, Hermann, Paris, 1958. | MR 102797 | Zbl 0080.16201

[Gr1] A. Grothendieck, Geometrie formelle et geometrie algebrique, Seminaire Bourbaki, Exp. 182, Mai 1959. | Numdam | Zbl 0229.14005

[Gr2] A. Grothendieck, Techniques de construction et theoremes d'existence en geometrie algebrique, IV: Les schemas de Hilbert, Seminaire Bourbaki, 1960/1961, no. 221. | Numdam | Zbl 0236.14003

[Gr3] A. Grothendieck, Local Cohomology, Lecture Notes in Math. 41, Springer-Verlag, New York, 1967. | MR 224620 | Zbl 0185.49202

[Green] M. Green, Quadrics of rank four in the ideal of the canonical curve, Inv. Math. 75 (1984), 84-104. | Zbl 0542.14018

[H] R. Hartshorne, Algebraic Geometry, Springer-Verlag, New York, 1977. | MR 463157 | Zbl 0367.14001

[K1] G. Kempf, On the geometry of a theorem of Riemann, Ann. Math. 98 (1973), 178-185. | MR 349687 | Zbl 0275.14023

[K2] G. Kempf, Schubert methods with an application to algebraic curves, Stichting Mathematisch Centrum, Amsterdam, 1971. | Zbl 0223.14018

[K3] G. Kempf, Abelian Integrals, Monografias del Instituto de Matemáticas 13, Universidad Nacional Autónoma de México, 1983. | MR 743421 | Zbl 0541.14023

[K4] G. Kempf, Deformations of symmetric products, Riemann Surfaces and Related Topics: Proceedings of the 1978 Stony Brook Conference, Annals of Math. Studies 97, Princeton Univ. Press, 1981, 319-341. | MR 624823 | Zbl 0465.14013

[K5] G. Kempf, The equations defining a curve of genus 4, Proc. A.M.S. 97, no. 2, (1986), 219-225. | MR 835869 | Zbl 0595.14021

[Ka] S. Katz, Infinitesimal deformations of manifolds with submanifolds, unpublished type-script, 4 pp.

[L-S] S. Lichtenbaum and M. Schlessinger, The cotangent complex of a morphism, Trans. A.M.S. 128 (1967), 41-70. | MR 209339 | Zbl 0156.27201

[M1] D. Mumford, Geometric Invariant Theory, Springer-Verlag, New York, 1965. | MR 214602 | Zbl 0147.39304

[M2] D. Mumford, Abelian Varieties, Oxford Univ. Press, 1970. | MR 282985 | Zbl 0223.14022

[M3] D. Mumford, Prym Varieties I, in Contributions to Analysis, Academic Press, New York, 1974, 325-350. | MR 379510 | Zbl 0299.14018

[M4] D. Mumford, Curves and their Jacobians, Univ. of Michigan Press, Ann Arbor, 1975. | MR 419430 | Zbl 0316.14010

[Mat] T. Matsusaka, On a characterization of a Jacobian variety, Mem. Coll. Sci. Kyoto, Series A, 32 (1959), 1-19. | MR 108497 | Zbl 0094.34103

[Mayer] A. Mayer, unpublished manuscript on constructive approaches to the Schottky and Torelli problems, circa 1965, 42 pages.

[O] F. Oort, Finite group schemes, local moduli for abelian varieties, and lifting problems, Algebraic Geometry, Oslo 1970, Wolters-Noordhoff, Groningen, 1972, 223-254. | Zbl 0239.14018

[O-S] F. Oort and J. Steenbrink, The local Torelli problem for algebraic curves, Journées de Géométrie Algébrique d'Angers 1979, Sijthoff & Noordhoff, Alphen aan den Rijn, 1980, 157-204. | MR 605341 | Zbl 0444.14007

[R] D.S. Rim, Formal deformation theory, Exp. VI, in Groupes de Monodromie en Géométrie Algébrique, Lecture Notes in Math. 288, Springer-Verlag, New York, 1972, 32-132. | Zbl 0246.14001

[S1] M. Schlessinger, Infinitesimal deformation of singularities, Harvard Thesis, 1964.

[S2] M. Schlessinger, Functors of Artin rings, Trans. A.M.S. 130 (1968), 208-222. | MR 217093 | Zbl 0167.49503

[S3] M. Schlessinger, Rigidity of quotient singularities, Invent. Math. 14 (1971), 17-26. | MR 292830 | Zbl 0232.14005

[S-D] B. Saint-Donat, On Petri's analysis of the linear system of quadrics through a canonical curve, Math. Ann. 206 (1973), 157-175. | MR 337983 | Zbl 0315.14010

[S-V1] R. Smith and R. Varley, Tangent cones to discriminant loci for families of hypersurfaces, Trans. A.M.S. 307 (1988), 647-674. | MR 940221 | Zbl 0674.14026

[S-V2] R. Smith and R. Varley, Deformations of singular points on theta divisors, Theta Functions- Bowdoin 1987, Proceedings Symp. Pure Math. vol. 49, Part I, A.M.S., 1989, 571-579. | Zbl 0702.14001

[V] R. Varley, unpublished summary of results on deformations of theta divisors, 1982, 3 pp.

[W] G. Welters, Polarized abelian varieties and the heat equations, Comp. Math. 49 (1983), 173-194. | Numdam | MR 704390 | Zbl 0576.14042