相关论文: Algebraic dimension of twistor spaces whose fundam…

We study the algebraic dimension of twistor spaces of positive type over $4\bbfP^2$. We show that such a twistor space is Moishezon if and only if its anticanonical class is not nef. More precisely, we show the equivalence of being…

It is shown that there exists a twistor space on the $n$-fold connected sum of complex projective planes $n\mathbb{CP}^2$, whose algebraic dimension is one and whose general fiber of the algebraic reduction is birational to an elliptic…

In this paper we explicitly construct Moishezon twistor spaces on nCP^2 for arbitrary n>1 which admit a holomorphic C*-action. When n=2, they coincide with Y. Poon's twistor spaces. When n=3, they coincide with the one studied by the author…

In this note, we investigate pluri-half-anticanonical systems on the so called LeBrun twistor spaces. We determine its dimension, the base locus, structure of the associated rational map, and also structure of general members, in precise…

We exploit techniques from classical (real and complex) algebraic geometry for the study of the standard twistor fibration $\pi:\mathbb{CP}^{3}\to S^{4}$. We prove three results about the topology of the twistor discriminant locus of an…

We investigate the structure of a variety of new Moishezon twistor spaces, by utilizing the pluri-half-anti-canonical map from the twistor spaces. Each of these twistor spaces is bimeromorphic to a double covering of a scroll of planes over…

In a recent paper (math.DG/0701278) we constructed a series of new Moishezon twistor spaces which is a kind of variant of the famous LeBrun twistor spaces. In this paper we explicitly give projective models of another series of Moishezon…

We continue to study twistor spaces on the connected sum of four complex projective planes, whose anticanonical map is of degree two over the image. In particular, we determine the defining equation of the branch divisor of the…

In four spacetime dimensions, the classically integrable self-dual sectors of gauge theory and gravity have associated chiral algebras, which emerge naturally from their description in twistor space. We show that there are similar chiral…

Given an integer n greater of equal to 3, we investigate the minimal dimension of a subalgebra of M_n(K) with a trivial centralizer. It is shown that this dimension is 5 when n is even and 4 when it is odd. In the latter case, we also…

We study the algebraic dimension a(X) of a compact hyperkaehler manfold of dimension 2n. We show that a(X) is at most n unless X is projective. If a compact Kaehler manifold with algebraic dimension 0 and Kodaira dimension 0 has a minimal…

It is shown that, over a field of characteristic not $2$, the dimension of an anisotropic quadratic Pfister form of trivial total signature is at most twice the dimension of some central division algebra of exponent $2$. The proof is based…

We provide a simple algebraic construction of the twistor spaces of arbitrary Joyce's self-dual metrics on the 4-manifold H^2 x T^2 that extend smoothly to nCP^2, the connected sum of complex projective planes. Indeed, we explicitly realize…

We establish a Penrose-Ward transform yielding a bijection between holomorphic principal 2-bundles over a twistor space and non-Abelian self-dual tensor fields on six-dimensional flat space-time. Extending the twistor space to supertwistor…

In this paper we classify all Moishezon twistor spaces on 4CP^2. The classification is given in terms of the structure of the anticanonical system of the twistor spaces. We show that the anticanonical map satisfies one of the following…

It is well known that a purely inseparable field extension $L/F$ with some extra property and degree $[L:F]=4$ determines a Clifford parallelism on the set of lines of the three-dimensional projective space over $F$. By extending the ground…

In characteristic two, it is shown that a central simple algebra of degree equal to a power of two with anisotropic orthogonal involution is totally decomposable, if it becomes either anisotropic or metabolic over all extensions of the…

For any finitely dimensional associative algebra with global dimension $\leq 2$, we show that there is an embedding from the twisted Ringel-Hall algebra to the Brigeland's Ringel-Hall algebra. In particular, this result is true for tilted…

Let X be a complex projective n-dimensional manifold of general type, whose canonical system is composite with a pencil. If the Albanese map is generically finite, but not surjective, or if the irregularity is strictly larger than n and the…

The recently introduced anomaly-free twistor string in four dimensions is shown to be defined not just in flat but also in curved twistor space. Further, arguments are given that the classical limit of the corresponding string field theory,…