Integral Symmetric Bilinear Forms and Some of Their Applications

We set up the technique of discriminant-forms, which allows us to transfer many results for unimodular symmetric bilinear forms to the nonunimodular case and is convenient in calculations. Further, these results are applied to Milnor's quadratic forms for singularities of holomorphic functions and also to algebraic geometry over the reals. Bibliography: 57 titles.

[1]  V. I. Arnol'd,et al.  Distribution of ovals of the real plane of algebraic curves, of involutions of four-dimensional smooth manifolds, and the arithmetic of integer-valued quadratic forms , 1971 .

[2]  S. Lang.  Algebraic Number Theory , 1971 .

[3]  M. Kneser,et al.  Quadratische Formen und Verschlingungsinvarianten von Knoten , 1953 .

[4]  Alan Durfee.  Bilinear and quadratic forms on torsion modules , 1977 .

[5]  I. Pjateckiĭ-Šapiro,et al.  A TORELLI THEOREM FOR ALGEBRAIC SURFACES OF TYPE K3 , 1971 .

[6]  I. Dolgachev.  Quotient-conical singularities on complex surfaces , 1974 .

[7]  I. Dolgachev.  Automorphic forms and quasihomogeneous singularities , 1975 .

[8]  V. Rokhlin.  Two-dimensional submanifolds of four-dimensional manifolds , 1971 .

[9]  M. Eichler,et al.  Quadratische Formen und orthogonale Gruppen , 1952 .

[10]  V. I. Arnol’d.  Index of a singular point of a vector field, the Petrovskii — Oleinik inequality, and mixed hodge structures , 1978 .

[11]  D A Gudkov,et al.  THE TOPOLOGY OF REAL PROJECTIVE ALGEBRAIC VARIETIES , 1974 .

[12]  A. Gabrielov.  Intersection matrices for certain singularities , 1973 .

[13]  G. N. Tjurina.  THE TOPOLOGICAL PROPERTIES OF ISOLATED SINGULARITIES OF COMPLEX SPACES OF CODIMENSION ONE , 1968 .

[14]  C. Wall.  Quadratic Forms on Finite Groups II , 1972 .

[15]  J. H. M. Steenbrink,et al.  Mixed Hodge Structure on the Vanishing Cohomology , 1977 .

[16]  Vladimir I. Arnold,et al.  CRITICAL POINTS OF SMOOTH FUNCTIONS AND THEIR NORMAL FORMS , 1975 .

[17]  Eduard Looijenga.  The discriminant of a real simple singularity , 1977 .

[18]  V. A. Rokhlin,et al.  Complex orientations of real algebraic curves , 1974 .

[19]  D. Gudkov,et al.  Periodicity of euler characteristic of real algebraic (M — 1)-manifolds , 1973 .

[20]  C. Wall.  Quadratic forms on finite groups, and related topics , 1963 .

[21]  I. Petrowsky,et al.  On the Topology of Real Plane Algebraic Curves , 1938 .

[22]  A. Harnack,et al.  Ueber die Vieltheiligkeit der ebenen algebraischen Curven , 1876 .

[23]  Felix Klein.  Eine neue Relation zwischen den Singularitäten einer algebraischen Curve , 1876 .

[24]  On Witt's theorem for unimodular quadratic forms. II. , 1968 .

[25]  J. Steenbrink.  Intersection form for quasi-homogeneous singularities , 1977 .

[26]  V. Rokhlin.  Congruence modulo 16 in Hilbert's sixteenth problem. II , 1973 .

[27]  M. Kneser.  Klassenzahlen indefiniter quadratischer Formen in drei oder mehr Veränderlichen , 1956 .

[28]  V. Kulikov.  Degenerate elliptic curves and resolution of uni- and bimodal singularities , 1975 .

[29]  C. Siegel,et al.  Uber Die Analytische Theorie Der Quadratischen Formen III , 1935 .

[30]  B. Saint-Donat.  Projective Models of K - 3 Surfaces , 1974 .