Linear symmetric determinantal hypersurfaces

Michigan Mathematical Journal

Volumn 54, Issue 1, 2006, Pages 117-156

  Pintkowski, Jens ^a  

^a JOHANNES GUTENBERG UNIVERSITY   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 33744747550     PISSN: 00262285     EISSN: None     Source Type: Journal    
DOI: 10.1307/mmj/1144437441     Document Type: Article

References (33)

1. [AGV] V. Arnold, S. Gusein-Zade, and A. Varchenko, Singularities of differentiable maps, vol. I, Monogr. Math., 82, Birkhäuser, Boston, 1985.
2. [At] M. Atkinson, Primitive space of matrices of bounded rank, II, J. Austral. Math. Soc. Ser. A 34 (1983), 306-315.
3. [B] W. Barth, Moduli of vector bundles on the projective plane, Invent. Math. 42 (1977), 63-91.
4. [BPV] W. Barth, C. Peters, and A. Van de Ven, Compact complex surfaces, Ergeb. Math. Grenzgeb. (3), 4, Springer-Verlag, Berlin, 1984.
5. [Be] A. Beauville, Deteminantal hypersurfaces, Michigan Math. J. 48 (2000), 39-64.
6. [BrW] J. Bruce and C. Wall, On the classification of cubic surfaces, J. London Math. Soc. (2) 19 (1979), 245-256.
7. [C] F. Catanese, Babbage's conjecture, contact of surfaces, symmetric determinantal varieties and applications, Invent. Math. 63 (1981), 433-465.
8. [Ca] A. Cayley, A memoir on quartic surfaces, Proc. London Math. Soc. 3 (1869-1871), 19-69.
9. [Co] F. Cossec, Reye congruences, Trans. Amer. Math. Soc. 280 (1983), 737-751.
10. [CoD] F. Cossec and I. Dolgachev, Enriques surfaces I, Progr. Math., 76, Birkhäuser, Boston, 1989.
11. [De] A. Degtyarev, Classification of quartic surfaces that have a nonsimple singular point, Math. USSR-Izv. 35 (1990), 607-627.
12. [Di] A. Dixon, Note on the reduction of a ternary quartic to a symmetrical determinant, Proc. Cambridge Phil. Soc. 11 (1900-1902), 350-351.
13. [Eb] W. Ebeling, Funktionentheorie, Differentialtopologie und Singularitäten, Vieweg, Braunschweig, 2001.
14. [E1] D. Eisenbud, Homological algebra on a complete intersection with an application to group representations, Trans. Amer. Math. Soc. 260 (1980), 35-64.
15. [E2] _, Commutative algebra. With a view toward algebraic geometry, Grad. Texts in Math., 150, Springer-Verlag, New York, 1995.
16. [FPi] G. Fischer and J. Piontkowski, Ruled varieties, Adv. Lectures Math., Vieweg, Braunschweig, 2001.
17. [Ga] F. Gantmacher, Matrizentheorie, Springer-Verlag, Berlin, 1986.
18. [Ha] J. Harris, Algebraic geometry, Grad. Texts in Math., 133, Springer-Verlag, New York, 1992.
19. [HTu] H. Harris and L. Tu, On symmetric and skew-symmetric determinantal varieties, Topology 30 (1984), 71-84.
20. [He] L. Hesse, Über die Elimination der Variabeln aus drei algebraischen Gleichungen von zweiten Grad mit zwei Variablen, J. Reine Angew. Math. 28 (1844), 68-96.
21. [KaN] M. Kato and I. Naruki, Depth of rational double points on quartic surfaces, Proc. Japan Acad. Ser. A Math. Sci. 58 (1982), 72-75.
22. [KU1] S. Kleiman and B. Ulrich, Gorenstein algebras, symmetric matrices, self-linked ideals, and symbolic powers, Trans. Amer. Math. Soc. 349 (1997), 4973-5000.
23. [L] E. Looijenga, On the semi-universal deformation of a simple elliptic hypersurface singularity. Part II: The discriminant, Topology 17 (1978), 23-40.
24. [M-B] T. Meyer-Brandis, Berührungssysteme und symmetrische Darstellungen ebener Kurven, Diplomarbeit, Mainz, 1998.
25. [N] V. Nikulin, Integer symmetric bilinear forms and some of their applications, Izv. Akad. Nauk SSSR Ser. Mat. 43 (1979), 111-177.
26. [R] M. Reid, Chapters on algebraic surfaces, Complex algebraic geometry (Park City, 1993), IAS/Park City Math. Ser., 3, pp. 3-159, Amer. Math. Soc., Providence, RI, 1997.
27. [S] G. Salmon, Solid geometry, 2nd ed., 1865.
28. [U1] T. Urabe, Elementary transformations of Dynkin graphs and singularities on quartic surfaces, Invent. Math. 87 (1987), 549-573.
29. [U2] _, Tie transformations of Dynkin graphs and singularities on quartic surfaces, Invent. Math. 100 (1990), 207-230.
30. [U3] _, Dynkin graphs and quadrilateral singularities, Lecture Notes in Math., 1548, Springer-Verlag, Berlin, 1993.
31. [T] O. Taussky, Nonsingular cubic curves as determinantal loci, J. Math. Phys. Sci. 21 (1987), 665-678.
32. [Y] J.-G. Yang, Enumeration of combinations of rational double points on quartic surfaces, Singularities and complex geometry (Beijing, 1994), AMS/IP Stud. Adv. Math., 5, pp. 275-312, Amer. Math. Soc., Providence, RI, 1997.
33. [Yo] Y. Yoshino, Cohen-Macaulay modules over Cohen-Macaulay rings, London Math. Soc. Lecture Note Ser., 146, Cambridge Univ. Press, 1990.