相关论文: Twistor lines on Nagata threefold

We study the geometry of families of hypersurfaces in Eguchi-Hanson space that arise as complex line bundles over curves in $S^2$ and are three-dimensional, non-compact Riemannian manifolds, which are foliated in Hopf tori for closed…

We construct two matrix models from twistor string theory: one by dimensional reduction onto a rational curve and another one by introducing noncommutative coordinates on the fibres of the supertwistor space P^(3|4)->CP^1. We comment on the…

We study the set of rational curves of a certain topological type in general members of certain families of Calabi-Yau threefolds. For some families we investigate to what extent it is possible to conclude that this set is finite. For other…

We classify families of free rational curves on all smooth Fano threefolds over the complex numbers. In particular, we prove the family of very free rational curves representing any fixed numerical curve class is either irreducible or…

A hyperk\"ahler manifold $M$ has a family of induced complex structures indexed by a two-dimensional sphere $S^2 \cong \mathbb{CP}^1$. The twistor space of $M$ is a complex manifold $Tw(M)$ together with a natural holomorphic projection…

Families of vector-like deformed relativistic quantum phase spaces and corresponding realizations are analyzed. Method for general construction of star product is presented. Corresponding twist, expressed in terms of phase space…

We study the flat CR twistor model $Q^{2,2}\subset \mathbb{CP}^3$ by explicit projective methods. Using the anti-holomorphic involution $j$ associated with the twistor fibration, we classify the projective lines contained in $Q^{2,2}$ into…

In this paper, we study the geometry of trisections on certain rational elliptic surfaces. We utilize Mumford representations of semi-reduced divisors in order to construct trisections and related plane curves with interesting properties…

An eight-parametric family of complex connections on a class complex manifolds with Norden metric is introduced. The form of the curvature tensor with respect to each of these connections is obtained. The conformal group of the considered…

Let $X=\overline{X}-D$ be a smooth quasi-projective curve. In arXiv:2110.12300 we constructed a Deligne-Hitchin modui space with Hecke gauge groupoid for connections of rank $2$. We extend this construction to the case of any rank $r$,…

In this paper, we provide a correspondence between certain 5-dimensional complex spacetimes and 4-dimensional twistor spaces. The spacetimes are almost contact manifolds whose curvature tensor satisfies certain conditions. By using the…

This article contains a compression of results from alg-geom/9501001, with most proofs omitted. We prove that every two points of the connected moduli space of holomorphically symplectic manifolds can be connected with so-called ``twistor…

New families of algebras and DG algebras with two simple modules are introduced and described. Using the twisted tensor product operation, we prove that such algebras have finite global dimension, and the resulting DG algebras are smooth.…

We find geometric conditions on a four-dimensional Hermitian manifold endowed with a metric connection with totally skew-symmetric torsion under which the complex structure is a harmonic map from the manifold into its twistor space…

We develop in detail the theory of c-projective geometry, a natural analogue of projective differential geometry adapted to complex manifolds. We realise it as a type of parabolic geometry and describe the associated Cartan or tractor…

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…

Given a path geometry on a surface $\mathcal{U}$, we construct a causal structure on a four-manifold which is the configuration space of non-incident pairs (point, path) on $\mathcal{U}$. This causal structure corresponds to a conformal…

We have established a 1-1 correspondence between a solution of the universal Whitham hierarchy and a twistor space. The twistor space consists of a complex surface and a family of complex curves together with a meromorphic 2-form. The…

In this largely expository note, we explain some recent progress on new cycles on Shimura varieties and Rapoport-Zink spaces, (twisted) arithmetic fundamental lemma, and arithmetic analogs of relative Langlands program. We explain related…

Let E be a plane rational curve defined over complex numbers which has only locally irreducible singularities. The Coolidge-Nagata conjecture states that E is rectifiable, i.e. it can be transformed into a line by a birational automorphism…