Related papers: Twistors, quartics, and del Pezzo fibrations

The purpose of this note is to establish a direct link between the theory of unexpected hypersurfaces and varieties with defective osculating behavior. We identify unexpected plane curves of degree 4 as sections of a rational surface X of…

This paper presents a worldsheet theory describing holomorphic maps to twistor space with N fermionic directions. The theory is anomaly free when N=8. Via the Penrose transform, the vertex operators correspond to an N=8 Einstein…

In this paper we prove a conjecture on the dimension of linear systems, with base points of multiplicity 2 and 3, on an Hirzebruck surface.

According to one of many equivalent definitions of twistors a (null) twistor is a null geodesic in Minkowski spacetime. Null geodesics can intersect at points (events). The idea of Penrose was to think of a spacetime point as a derived…

In the past three decades, the study of rhombus tilings and domino tilings of various plane regions has been a thriving subfield of enumerative combinatorics. Physicists classify such work as the study of dimer covers of finite graphs. In…

We study the groups of automorphisms of rational algebraic surfaces that admit a relatively minimal pencil of curves of arithmetic genus one over an algebraically closed field of arbitrary characteristic. In particular, we classify such…

The two-twistor formulation of particle mechanics in D-dimensional anti-de Sitter space for D=4,5,7, which linearises invariance under the AdS isometry group Sp(4;K) for K=R,C,H, is generalized to the massless N-extended "spinning…

The surfaces considered are real, rational and have a unique smooth real $(-2)$-curve. Their canonical class $K$ is strictly negative on any other irreducible curve in the surface and $K^2>0$. For surfaces satisfying these assumptions, we…

We classify del Pezzo non-commutative surfaces that are finite over their centres and have no worse than canonical singularities. Using the minimal model program, we introduce the minimal model of such surfaces. We first classify the…

This paper presents a new result concerning the distribution of 2-Selmer ranks in the quadratic twist family of an elliptic curve over an arbitrary number field K with a single point of order two that does not have a cyclic 4-isogeny…

We provide minimal constructions of meanders with particular combinatorics. Using these meanders, we give minimal constructions of hyperelliptic pillowcase covers with a single horizontal cylinder and simultaneously a single vertical…

Particle and string actions on coset spaces typically lack a quadratic kinetic term, making their quantization difficult. We define a notion of twistors on these spaces, which are hypersurfaces in a vector space that transform linearly…

The geometry of the Fano scheme of maximal linear spaces contained in the base locus of a pencil of quadrics has been studied by algebraic geometers when the base field is algebraically closed. In this paper, we work over an arbitrary base…

We prove that the integral points are potentially Zariski dense in the complement of a reduced effective singular anticanonical divisor in a smooth del Pezzo surface, with the exception of $\mathbb{P}^2$ minus three concurrent lines (for…

We introduce a theoretical framework for the new concept of three-dimensional (3D) twistronics by developing a generalized Bloch band theory for 3D layered systems with a constant twist angle $\theta$ between successive layers. Our theory…

We give a new geometric proof of the classification of $T$-polygons, a theorem originally due to Kasprzyk, Nill and Prince, using ideas from mirror symmetry. In particular, this gives a completely geometric proof that any two toric…

Recently, we introduced a new class of shapes, called soft cells which fill space as soft tilings without gaps and overlaps while minimizing the number of sharp corners. We introduced the edge bending algorithm that deforms a polyhedral…

Poisson structures of divisor-type are those whose degeneracy can be captured by a divisor ideal, which is a locally principal ideal sheaf with nowhere-dense quotient support. This is a large class of Poisson structures which includes all…

Patchworking theorems serve as a basic element of the correspondence between tropical and algebraic curves, which is a core of the tropical enumerative geometry. We present a new version of a patchworking theorem which relates plane…

Let $Y$ be the del Pezzo $4$-fold defined by the linear section $\textrm{Gr}(2,5)$ by $\mathbb{P}^7$. In this paper, we classify the type of normal bundles of lines in $Y$ and describe its parameter space. As a corollary, we obtain the…