The equations of conjugacy classes of nilpotent matrices.
The equations of space curves on a quadric.
The homogeneous ideals of curves in a double plane have been studied by Chiarli, Greco, Nagel. Completing this work we describe the equations of any curve that is contained in some quadric. As a consequence, we classify the Hartshorne-Rao modules of such curves.
The equations of the abelian surfaces embedded in ...4 (...).
The equivariant fundamental group, uniformization of real algebraic curves, and global complex analytic coordinates on Teichmüller spaces
The Etale Homotopy Theorie of a Geometric Fibration.
The Euler characteristic of algebraic complete intersections.
The Euler characteristic of the moduli space of curves.
The Euler characteristic of varieties realized as the complete intersection of toric hypersurfaces.
The Euler number of the normalization of an algebraic threefold with ordinary singularities
By a classical formula due to Enriques, the Euler number χ(X) of the non-singular normalization X of an algebraic surface S with ordinary singularities in P³(ℂ) is given by χ(X) = n(n²-4n+6) - (3n-8)m + 3t - 2γ, where n is the degree of S, m the degree of the double curve (singular locus) of S, t is the cardinal number of the triple points of S, and γ the cardinal number of the cuspidal points of S. In this article we shall give a similar formula for an algebraic threefold with ordinary singularities...
The Euler series of restricted Chow varieties
The existence of algebraic surfaces with preassigned Chern numbers.
The existence of elliptic fibre space structures on Calabi-Yau threefolds.
The existence of equivariant pure free resolutions
Let be a polynomial ring in variables and let be a strictly increasing sequence of integers. Boij and Söderberg conjectured the existence of graded -modules of finite length having pure free resolution of type in the sense that for the -th syzygy module of has generators only in degree .This paper provides a construction, in characteristic zero, of modules with this property that are also -equivariant. Moreover, the construction works over rings of the form where is a polynomial...
The existence of higher logarithms
The existence of infinitely many supersingular primes for every elliptic curve over Q.
The explicit reciprocity law and the cohomology of Fontaine-Messing
The exponent of an abelian subvariety.
The Extension of Regular and Rational Embeddings.
The Fano surface of the Gushel threefold
The Fedoryuk Condition and the Łojasiewicz Exponent near a Fibre of a Polynomial
We give a description of the set of points for which the Fedoryuk condition fails in terms of the Łojasiewicz exponent at infinity near a fibre of a polynomial.