Self-adjoint determinantal representations of real plane curves
Tài liệu tham khảo
Catanese, F.: Babbage's conjecture, contact of surfaces, symmetric determinantal varieties and applications. Invent. Math.63, 433–465 (1981)
Cook, A.J., Thomas, A.D.: Line bundles and homogeneous matrices. Q. J. Math. Oxf., II. Ser.30, 423–429 (1979)
Dixon, A.C.: Note on the reduction of a ternary quartic to a symmetrical determinant. Proc. Camb. Phil. Soc.2, 350–351 (1900–1902)
Dubrovin, B.A.: Matrix finite zone operators. Contemporary probl. math. (Itogi Nauki i Techniki)23, 33–78 (1983) (Russian)
Dubrovin, B.A., Natanzon, S.M.: Real two-zone solutions of the sine-Gordon equation. Funct. Anal. Appl.16, 21–33 (1982)
Fay, J.D.: Theta functions on Riemann surfaces. Berlin Heidelberg New York: Springer 1973
Gohberg, I., Lancaster, P., Rodman, L.: Matrices and indefinite scalar products. Basel: Birkhäuser, 1983
Griffiths, P., Harris, J.: Principles of algebraic geometry. New York: Wiley 1978
Gross, B.H., Harris, J.: Real algebraic curves. Ann. Sci. Ec. Norm. Supér., IV. Ser.14, 157–182 (1981)
Husemoller, D., Milnor, J.: Symmetric bilinear forms. Berlin Heidelberg New York: Springer 1973
Igusa, J.I.: Theta functions. Berlin Heidelberg New York: Springer 1972
Livšic, M.S.: Cayley-Hamilton theorem, vector bundles and divisors of commuting operators. Integral Equations Oper. Theory6, 250–273 (1983)
Natanzon, S.M.: Prymians of real curves and their applications to the effectivization of Schrödinger operators. Funct. Anal. Appl.23, 33–45 (1989)
Nuij, W.: A note on hyperbolic polynomials. Math. Scand.23, 69–72 (1968)
Rokhlin, V.A.: Complex topological characteristics of real algebraic curves. Russ. Math. Surv.33, 85–98 (1978)
Room, T.G.: The geometry of determinantal loci. Cambridge: Cambridge Univ. Press 1938
Vinnikov, V.: Determinantal representations of real cubics and canonical forms of corresponding triples of matrices. In: Mathematical theory of networks and systems, Fuhrmann, P.A., (ed.), Berlin Heidelberg New York: Springer 1984
Vinnikov, V.: Self-adjoint determinantal representations of real irreducible cubics. In: Operator theory and systems, Bart, H., Gohberg, I., Kaashoek, M.A. (eds.), Boston: Birkhäuser 1986
Vinnikov, V.: Complete description of determinantal representations of smooth irreducible curves. Lin. Alg. Appl.125, 103–140 (1989)
Vinnikov, V.: Elementary transformations of determinantal representations of algebraic curves. Linear Algebra Appl.135, 1–18 (1990)
Vinnikov, V.: Commuting nonselfadjoint operators and algebraic curves. Proceedings of the Workshop on Operator Theory and Complex Analysis (Sapporo, Japan, 1991), Boston: Birkhäuser 1992
Viro, O. Ya.: Progress in the topology of real algebraic varieties over the last six years. Russ. Math. Surv.41, 55–82 (1986)
Wall, C.T.C.: Nets of quadrics, and theta-characteristics of singular curves. Philos. Trans. R. Soc. Lond.,A 289, 229–269 (1978)
Weichold, G.: Über symmetrische Riemannsche Flächen. Z. Math. Phys.28, 321–354 (1883)