Related papers: Kummer quartic double solids
This is, mostly, a survey of results about the birational geometry of rationally connected manifolds, using rational curves analogous to lines in ${\mathbb P}^n$ ({\it quasi-lines}). Various characterizations of a Zariski neighbourhood of a…
We investigate the geometric and conformally equivariant quantizations of the supercotangent bundle of a pseudo-Riemannian manifold $(M,g)$, which is a model for the phase space of a classical spin particle. This is a short review of our…
This note contains a solution to the following problem: reconstruct the definition field and the equation of a projective cubic surface, using only combinatorial information about the set of its rational points. This information is encoded…
We construct orbifolds with quasitoric boundary and show that they have stable almost complex structure. We show that a quasitoric orbifold is complex cobordant to finite disjoint copies of complex orbifold projective spaces. Finally some…
In this paper we survey results and recent progresses on the equivariant bordism classification of 2-torus manifolds and unitary toric manifolds.
K3 surfaces have been studied from many points of view, but the positivity of the cotangent bundle is not well understood. In this paper we explore the surprisingly rich geometry of the projectivised cotangent bundle of a very general…
A general linear determinantal quartic in $\mathbb{P}^4$ is nodal, non-$\mathbb{Q}$-factorial and rational. We show that the family $\mathcal{F}$ of such quartics also contains rational $\mathbb{Q}$-factorial quartics, and that a generic…
Parametric Cartan theory of exterior differential systems, and explicit cohomology of projective manifolds reveal united rationality features of differential algebraic geometry.
Framed quiver moduli parametrize stable pairs consisting of a quiver representation and a map to a fixed graded vector space. Geometric properties and explicit realizations of framed quiver moduli for quivers without oriented cycles are…
Let k be an arbitrary field of characteristic zero. In this paper we study quotients of k-rational conic bundles over projective line by finite groups of automorphisms. We construct smooth minimal models for such quotients. We show that any…
We investigate geometric properties of surfaces given by certain formulae. In particular, we calculate the singular curvature and the limiting normal curvature of such surfaces along the set of singular points consisting of singular points…
We prove that the moduli space of double covers ramified at two points $\mathcal{R}_{g,2}$ is uniruled for $3\leq g\leq 6$ and of general type for $g\geq 16$. Furthermore, we consider Prym-canonical divisorial strata in the moduli space…
We study surfaces constructed from groups of units in quaternion orders $\Lambda$ over the integers in real quadratic fields k. A short presentation of some general theory of such surfaces is given, in particular, we construct certain…
We develop a quasisymmetric analogue of the theory of Schubert cycles, building off of our previous work on a quasisymmetric analogue of Schubert polynomials and divided differences. Our constructions result in a natural geometric…
We consider the problem of counting the number of rational points on the family of Kummer surfaces associated with two non-isogenous elliptic curves. For this two-parameter family we prove Manin's unity, using the presentation of the Kummer…
Equivariant quantization is a new theory that highlights the role of symmetries in the relationship between classical and quantum dynamical systems. These symmetries are also one of the reasons for the recent interest in quantization of…
We show for any oriented surface, possibly with a boundary, how to generalize Kramers-Wannier duality to the world of quantum groups. The generalization is motivated by quantization of Poisson-Lie T-duality from the string theory.…
We develop an equivariant version of the formalism of intermediate Jacobian torsor obstructions, and apply it to conic bundles over rational surfaces, quadric surface bundles over $\mathbb P^1$, and Fano threefolds.
A desmic quartic surface is a birational model of the Kummer surface of the self-product of an elliptic curve. We recall the classical geometry of these surfaces and study their analogs in arbitrary characteristic. Moreover, we discuss the…
Motivated by the power of subregion/subregion duality for constraining the bulk geometry in gauge/gravity duality, we pursue a comprehensive and systematic approach to the behavior of extremal surfaces under perturbations. Specifically, we…