Displaying similar documents to “Almost regular quaternary quadratic forms”

Decompositions of an Abelian surface and quadratic forms

Shouhei Ma (2011)

Annales de l’institut Fourier

Similarity:

When a complex Abelian surface can be decomposed into a product of two elliptic curves, how many decompositions does the Abelian surface admit? We provide arithmetic formulae for the number of such decompositions.

On the K-theory of tubular algebras

Dirk Kussin (2000)

Colloquium Mathematicae

Similarity:

Let Λ be a tubular algebra over an arbitrary base field. We study the Grothendieck group K 0 ( Λ ) , endowed with the Euler form, and its automorphism group A u t ( K 0 ( Λ ) ) on a purely K-theoretical level as in [7]. Our results serve as tools for classifying the separating tubular families of tubular algebras as in the example [5] and for determining the automorphism group A u t ( D b Λ ) of the derived category of Λ.

The higher transvectants are redundant

Abdelmalek Abdesselam, Jaydeep Chipalkatti (2009)

Annales de l’institut Fourier

Similarity:

Let A , B denote generic binary forms, and let 𝔲 r = ( A , B ) r denote their r -th transvectant in the sense of classical invariant theory. In this paper we classify all the quadratic syzygies between the { 𝔲 r } . As a consequence, we show that each of the higher transvectants { 𝔲 r : r ≥ 2 } is redundant in the sense that it can be completely recovered from 𝔲 0 and 𝔲 1 . This result can be geometrically interpreted in terms of the incomplete Segre imbedding. The calculations rely upon the Cauchy exact sequence of S L 2 -representations,...

On the remainder in the Weyl formula for the Euclidean disk

Yves Colin de Verdière (2010-2011)

Séminaire de théorie spectrale et géométrie

Similarity:

We prove a 2-terms Weyl formula for the counting function N ( μ ) of the spectrum of the Laplace operator in the Euclidean disk with a sharp remainder estimate O μ 2 / 3 .