The Maximal Rank Conjecture for Non-Special Curves in Ipn.
The membership problem for polynomial ideals in terms of residue currents
We find a relation between the vanishing of a globally defined residue current on and solution of the membership problem with control of the polynomial degrees. Several classical results appear as special cases, such as Max Nöther’s theorem, for which we also obtain a generalization. Furthermore there are some connections to effective versions of the Nullstellensatz. We also provide explicit integral representations of the solutions.
The meromorphic continuation of a zeta function of Weil and Igusa Type.
The Milnor fiber and the zeta function of the singularities of type
The Milnor Number and Deformations of Complex Curve Singularities.
The Milnor number of functions on singular hypersurfaces
The behaviour of a holomorphic map germ at a critical point has always been an important part of the singularity theory. It is generally known (cf. [5]) that we can associate an integer invariant - called the multiplicity - to each isolated critical point of a holomorphic function of many variables. Several years later it was noticed that similar invariants exist for function germs defined on isolated hypersurface singularities (see [1]). The present paper aims to show a simple approach to critical...
The minimal freee resolution of the homogeneous ideal of s general points in P4.
The Missing Seventh Circle.
The Modell-Weil groups of unirational quasi-elliptic surfaces in characteristic 3.
The modified diagonal cycle on the triple product of a pointed curve
Let be a curve over a field with a rational point . We define a canonical cycle . Suppose that is a number field and that has semi-stable reduction over the integers of with fiber components non-singular. We construct a regular model of and show that the height pairing is well defined where and are correspondences. The paper ends with a brief discussion of heights and -functions in the case that is a modular curve.
The modularity of the Barth-Nieto quintic and its relatives.
The moduli and the global period mapping of surfaces with : a counterexample to the global Torelli problem
The Moduli of Super-Null-Correlation Bundles on IP3.
The Moduli of Weierstrass Fibriations Over P1 .
The moduli scheme M (0, 2, 4) over IP3.
The Moduli Space of (3,3,3) Trilinear forms.
The Moduli Space of 3-Folds with K = 0 may Nevertheless be Irreducible.
The moduli space of commutative algebras of finite rank
The moduli space of rank- commutative algebras equipped with an ordered basis is an affine scheme of finite type over , with geometrically connected fibers. It is smooth if and only if . It is reducible if (and the converse holds, at least if we remove the fibers above and ). The relative dimension of is . The subscheme parameterizing étale algebras is isomorphic to , which is of dimension only . For , there exist algebras that are not limits of étale algebras. The dimension calculations...
The moduli space of curves of genus two covering elliptic curves.
The moduli space of Riemann surfaces is Kähler hyperbolic.