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On the stable equivalence problem for k[x,y]

Robert Dryło (2011)

Colloquium Mathematicae

L. Makar-Limanov, P. van Rossum, V. Shpilrain and J.-T. Yu solved the stable equivalence problem for the polynomial ring k[x,y] when k is a field of characteristic 0. In this note we give an affirmative solution for an arbitrary field k.

On the strange duality conjecture for abelian surfaces

Alina Marian, Dragos Oprea (2014)

Journal of the European Mathematical Society

We study Le Potier's strange duality conjecture for moduli spaces of sheaves over generic abelian surfaces. We prove the isomorphism for abelian surfaces which are products of elliptic curves, when the moduli spaces consist of sheaves of equal ranks and ber degree 1. The birational type of the moduli space of sheaves is also investigated. Generalizations to arbitrary product elliptic surfaces are given.

On the structure of Brieskorn lattice

Morihiko Saito (1989)

Annales de l'institut Fourier

We study the structure of the filtered Gauss-Manin system associated to a holomorphic function with an isolated singularity, and get a basis of the Brieskorn lattice Ω X , 0 n + 1 / d f d Ω X , 0 n + 1 over { { t - 1 } } such that the action of t is expressed by t v = A 0 + A 1 t - 1 v for two matrices A 0 , A 1 with A 1 semi-simple, where v = t ( v 1 ... v μ ) is the basis. As an application, we calculate the b -function of f in the case of two variables.

On the structure of linked 3-folds.

Aldo Biancofiore, Maria Lucia Fania (2001)

Revista Matemática Complutense

The structure of 3-folds in P6 which are generally linked via a complete intersection (f1,f2,f3) to 3-folds in P6 of degree d ≤ 5 is determined. We also give three new examples of smooth 3-folds in P6 of degree 11 and genus 9. These examples are obtained via liaison. The first two are 3-folds linked via a complete intersection (2,3,3) to 3-folds in P6 of degree 7: (i) the hyperquadric fibration over P1 and (ii) the scroll over P2. The third example is Pfaffian linked to a 3-dimensional quadric in...

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