Related papers: Some new rational Gushel fourfolds

In this article we will represent some ideas and a lot of new theorems in Euclidean plane geometry.

We construct new families of smooth Fano fourfolds with Picard rank 1, which contain cylinders, i.e., Zariski open subsets of form $Z\times A^1$, where $Z$ is a quasiprojective variety. The affine cones over such a fourfold admit effective…

A four-parameter class of exact asymptotically flat solutions of the Einstein-Maxwell equations involving only rational functions is presented. It is able to describe the exterior field of a slowly or rapidly rotating neutron star with…

We construct new examples of cubic polynomials with a parabolic fixed point that cannot be approximated by Misiurewicz polynomials. In particular, such parameters admit maximal bifurcations, but do not belong to the support of the…

We introduce tropical Newton-Puiseux polynomials admitting rational exponents. A resolution of a tropical hypersurface is defined by means of a tropical Newton-Puiseux polynomial. A polynomial complexity algorithm for resolubility of a…

We review some recent results on the modularity of non-rigid Calabi-Yau threefolds.

The normal connected sum construction of Gompf and the rational blowing-down technique of Fintushel - Stern are important tools in constructing symplectic 4-manifolds. In some cases, the 4-manifolds created this way are of Kahler type. In…

We investigate equivariant birational geometry of rational surfaces and threefolds from the perspective of derived categories.

This paper extends approach of recent author's paper devoted to special classes of exact solutions of the static Maxwell system in inhomogeneous isotropic media and new generalizations of the Cauchy-Riemann system in $\mathbb R^3$. Two…

We consider compact oriented four-manifolds with harmonic self-dual Weyl curvature in addition to a pinching condition.

Works by O'Grady allow to associate to a 2-dimensional Gushel-Mukai variety, which is a K3 surface, a double EPW sextic. We characterize the K3 surfaces whose associated double EPW sextic is smooth. As a consequence, we are able to produce…

We construct explicit equations of Cartwright-Steger and related surfaces.

We investigate the birational geometry of Deligne-Mumford stacks and define new birational invariants in this context.

We study the minimal genus problem for some smooth four-manifolds.

We develop and study the generalization of rational Schur algebras to the super setting. Similar to the classical case, this provides a new method for studying rational supermodules of the general linear supergroup $GL(m|n)$. Furthermore,…

Using an algebraic method for solving the wave equation in quantum mechanics, we encountered a new class of orthogonal polynomials on the real line. It consists of a four-parameter polynomial with continuous spectrum on the whole real line…

A new kind of diagrams is presented, showing the causal structure of bimetric interactions.

In this paper we study non-negatively curved and rationally elliptic GKM$_4$ manifolds and orbifolds. We show that their rational cohomology rings are isomorphic to the rational cohomology of certain model orbifolds. These models are…

A new family of analytically solvable quantum geometric models is proposed. The structure of the energy spectra as well as the form of the corresponding eigenfunctions are presented pointing out their main specific properties.

Exactly solvable rationally-extended radial oscillator potentials, whose wavefunctions can be expressed in terms of Laguerre-type exceptional orthogonal polynomials, are constructed in the framework of $k$th-order supersymmetric quantum…