A conic and an -quintic with a point at infinity.
A conjecture on Poincaré-Betti series of modules of differential operators on a generic hyperplane arrangement.
A construction of an abelian variety with a given endomorphism algebra
A construction of curves over finite fields
A Construction of Surfaces with pg = 1, q = 0 and 2...(K2) ...8. Counter Examples of the Global Torelli Theorem.
A continuous, constructive solution to Hilbert's 17th problem.
A contribution to the theory of tacnodal quartics
A converse to the Andreotti-Grauert theorem
The goal of this paper is to show that there are strong relations between certain Monge-Ampère integrals appearing in holomorphic Morse inequalities, and asymptotic cohomology estimates for tensor powers of holomorphic line bundles. Especially, we prove that these relations hold without restriction for projective surfaces, and in the special case of the volume, i.e. of asymptotic -cohomology, for all projective manifolds. These results can be seen as a partial converse to the Andreotti-Grauert...
A counterexample in the theory of local zeta functions.
A counterexample to a conjecture of Bass, Connell and Wright
Let F=X-H: → be a polynomial map with H homogeneous of degree 3 and nilpotent Jacobian matrix J(H). Let G=(G1,...,Gn) be the formal inverse of F. Bass, Connell and Wright proved in [1] that the homogeneous component of of degree 2d+1 can be expressed as , where T varies over rooted trees with d vertices, α(T)=CardAut(T) and is a polynomial defined by (1) below. The Jacobian Conjecture states that, in our situation, is an automorphism or, equivalently, is zero for sufficiently large d....
A counterexample to a conjecture of Drużkowski and Rusek
Let F = X + H be a cubic homogeneous polynomial automorphism from to . Let be the nilpotence index of the Jacobian matrix JH. It was conjectured by Drużkowski and Rusek in [4] that . We show that the conjecture is true if n ≤ 4 and false if n ≥ 5.
A Counterexample to a Conjecture of Zariski.
A counterexample to a conjecture on linear systems on .
A Counterexample to Artin Approximation With Respect to Subrings.
A counterexample to the strong real Jocobian conjecture.
A counterexample to the theorem of Beppo Levi in three dimensions.
A criterion for a rational projectively normal variety to be almost-factorial
A criterion for a variety to be cone.
A criterion for algebraicity of certain analytic elliptic surfaces.
A criterion for detecting m-regularity.