Some characterizaions of smooth, regular, and complete intersection algebras.
Some consequences of perversity of vanishing cycles
For a holomorphic function on a complex manifold, we show that the vanishing cohomology of lower degree at a point is determined by that for the points near it, using the perversity of the vanishing cycle complex. We calculate this order of vanishing explicitly in the case the hypersurface has simple normal crossings outside the point. We also give some applications to the size of Jordan blocks for monodromy.
Some Consequences of the Riemann Hypothesis for Varieties over Finite Fields.
Some Criteria for Finite and Infinite Monodromy of Plane Algebraic Curves.
Some Criteria for Rigidity of Noetherian Rings.
Some Curves in Abelian Varieties.
Some defective secant varieties to osculating varieties of Veronese surfaces.
We consider the k-osculating varietiesOk,d to the Veronese d?uple embeddings of P2. By studying the Hilbert function of certain zero-dimensional schemes Y ⊂ P2, we find the dimension of Osk,d, the (s?1)th secant varieties of Ok,d, for 3 ≤ s ≤ 6 and s = 9, and we determine whether those secant varieties are defective or not.
Some density results for curves with non-simple jacobians.
Some Elementary Theorem about Algebraic Cycles on Abelian Varieties.
Some elliptic function identities
Some enumerative properties of secants to non-singular projective schemes.
Some estimates from étale cohomology.
Some examples of 5 and 7 descent for elliptic curves over
We perform descent calculations for the families of elliptic curves over with a rational point of order or 7. These calculations give an estimate for the Mordell-Weil rank which we relate to the parity conjecture. We exhibit explicit elements of the Tate-Shafarevich group of order 5 and 7, and show that the 5-torsion of the Tate-Shafarevich group of an elliptic curve over may become arbitrarily large.
Some examples of Gorenstein liaison in codimension three.
Gorenstein liaison seems to be the natural notion to generalize to higher codimension the well-known results about liaison of varieties of codimension 2 in projective space. In this paper we study points in P3 and curves in P4 in an attempt to see how far typical codimension 2 results will extend. While the results are satisfactory for small degree, we find in each case examples where we cannot decide the outcome. This examples are candidates for counterexamples to the hoped-for extensions of codimension...
Some examples of torsion in the Griffiths group.
Some families of non-congruent numbers
Some finitely generated modules and cohomologies and the Jacobian conjecture
We show that the plane Jacobian conjecture is equivalent to finite generatedness of certain modules.
Some finiteness properties of the fundamental group of a smooth variety
Some finiteness theorems on Galois centralizers in pro-l mapping class groups.
Some functions related to the derivatives of the L-series of an elliptic curve at s=1