Results 31 to 40 of about 1,944,105 (329)
Hypercomplex Algebraic Geometry [PDF]
The Quarterly Journal of Mathematics, 1998 Let \({\mathbb H}=\{ r_0 + r_1i_1 + r_2i_2 + r_3i_3 \mid r_j\in{\mathbb R} \}\) be the skew field of quaternions which satisfy the following relations \[ \begin{aligned} i_1 i_2 &= -i_2 i_1=i_3,\qquad i_2 i_3=-i_3 i_2=i_1,\\ i_3 i_1 &= -i_1 i_3=i_2,\qquad i_1^2=i_2^2=i_3^2=-1.\end{aligned} \] Let \(U\subset{\mathbb H}^n\) be an open domain and \(f:U\to{
openaire +4 more sources
Good Codes From Generalised Algebraic Geometry Codes [PDF]
, 2010 Algebraic geometry codes or Goppa codes are defined with places of degree one. In constructing generalised algebraic geometry codes places of higher degree are used.
Ahmed, Mohammed Zaki +3 more
core +3 more sources
Complementary Dual Algebraic Geometry Codes [PDF]
IEEE Transactions on Information Theory, 2016 Linear complementary dual (LCD) codes are a class of linear codes introduced by Massey in 1964. LCD codes have been extensively studied in literature recently.
Sihem Mesnager +2 more
semanticscholar +1 more source
Stable rationality of higher dimensional conic bundles [PDF]
Épijournal de Géométrie Algébrique, 2018 We prove that a very general nonsingular conic bundle $X\rightarrow\mathbb{P}^{n-1}$ embedded in a projective vector bundle of rank $3$ over $\mathbb{P}^{n-1}$ is not stably rational if the anti-canonical divisor of $X$ is not ample and $n\geq 3$.
Hamid Ahmadinezhad, Takuzo Okada
doaj +1 more source
Limits of the trivial bundle on a curve [PDF]
Épijournal de Géométrie Algébrique, 2018 We attempt to describe the rank 2 vector bundles on a curve C which are specializations of the trivial bundle. We get a complete classifications when C is Brill-Noether generic, or when it is hyperelliptic; in both cases all limit vector bundles are ...
Arnaud Beauville
doaj +1 more source
The conjectures of Artin-Tate and Birch-Swinnerton-Dyer [PDF]
Épijournal de Géométrie Algébrique, 2022 We provide two proofs that the conjecture of Artin-Tate for a fibered surface is equivalent to the conjecture of Birch-Swinnerton-Dyer for the Jacobian of the generic fibre.
S. Lichtenbaum +2 more
doaj +1 more source
Information Decomposition and Synergy
Entropy, 2015 Recently, a series of papers addressed the problem of decomposing the information of two random variables into shared information, unique information and synergistic information.
Eckehard Olbrich +2 more
doaj +1 more source
Serre-invariant stability conditions and Ulrich bundles on cubic threefolds [PDF]
Épijournal de Géométrie Algébrique, 2023 We prove a general criterion which ensures that a fractional Calabi--Yau category of dimension $\leq 2$ admits a unique Serre-invariant stability condition, up to the action of the universal cover of $\text{GL}^+_2(\mathbb{R})$.
Soheyla Feyzbakhsh, Laura Pertusi
doaj +1 more source
Spherical subcategories in algebraic geometry [PDF]
, 2016 We study objects in triangulated categories which have a two-dimensional graded endomorphism algebra. Given such an object, we show that there is a unique maximal triangulated subcategory, in which the object is spherical.
Hochenegger, Andreas +2 more
core +2 more sources
Non-commutative algebraic geometry of semi-graded rings [PDF]
International journal of algebra and computation, 2016 In this paper we introduce the semi-graded rings, which extend graded rings and skew PBW extensions. For this new type of non-commutative rings we will discuss some basic problems of non-commutative algebraic geometry.
O. Lezama, Edward Latorre
semanticscholar +1 more source