Related papers: Some new rational Gushel fourfolds

We present new classes of permutation polynomials over finite fields.

Gushel-Mukai sixfolds are an important class of so-called Fano-K3 varieties. In this paper we show that they admit a multiplicative Chow-K\"unneth decomposition modulo algebraic equivalence and that they have the Franchetta property. As…

Are Fourier-Mukai equivalent cubic fourfolds birationally equivalent? We obtain an affirmative answer to this question for very general cubic fourfolds of discriminant 20, where we produce birational maps via the Cremona transformation…

We determine a new technique which allows the computation of the arithmetical rank of certain monomial ideals.

We describe a new method of constructing rational surfaces with given invariants in P^4 and present a family of degree 11 rational surfaces of sectional genus 11 with 2 six-secants that we found with this method.

We propose two conjectures on a moduli theoretic approach to constructing Lagrangian subvarieties of hyperk\"ahler varieties arising from the Kuznetsov components of cubic fourfolds or Gushel--Mukai fourfolds. Then we verify the conjectures…

We prove that if two very general cubic fourfolds are L-equivalent then they are isomorphic, and we observe that there exist special cubic fourfolds which are L-equivalent but not isomorphic. When the cubic fourfolds are very general in…

We classify $G$-solid rational surfaces over the field of complex numbers.

We prove that every Hassett's Noether-Lefschetz divisor of special cubic fourfolds contains a union of three codimension-two subvarieties, parametrizing rational cubic fourfolds, in the moduli space of smooth cubic fourfolds.

In the first part of this paper we will prove the Voevodsky's nilpotence conjecture for smooth cubic fourfolds and ordinary generic Gushel-Mukai fourfolds. Then, making use of noncommutative motives, we will prove the Voevodsky's nilpotence…

A new family of maximal curves over a finite field is presented and some of their properties are investigated.

New examples of noncommutative 4-spheres are introduced.

Beauville and Donagi proved in 1985 that the primitive middle cohomology of a smooth complex cubic fourfold and the primitive second cohomology of its variety of lines, a smooth hyperk\"ahler fourfold, are isomorphic as polarized integral…

We study rationality constructions for smooth complete intersections of two quadrics over nonclosed fields. Over the real numbers, we establish a criterion for rationality in dimension four.

We give a complete description for the dynamics of quadratic rational maps with coefficients in the completion of the field of formal Puiseux series.

Some special solutions to the multidimensional Lam\'e and Bourlet type equations are constructed in an explicit form.

In this paper, we introduce new generalizations of higher-order Changhee of the first and second kind. Moreover, we derive some new results for these numbers and polynomials. Furthermore, some interesting special cases of the generalized…

Some new Kasami type codes of higher relative dimension is introduced. Their weight distribution is determined.

A new relativistic invariant version of nonlinear Maxwell equations is offerred. Some properties of these equations are considered.

We discuss some examples of geometrically meaningful rational self-maps of moduli space of curves of low genus and homogeneous forms.