Related papers: Some new rational Gushel fourfolds

We prove that very general, dual Gushel-Mukai surfaces are not isomorphic, though derived and L-equivalent. We use this result to study two semiorthogonal decompositions for a family of Fano fourfolds of K3 type, answering a question by…

We introduce the notion of a categorical cone, which provides a categorification of the classical cone over a projective variety, and use our work on categorical joins to describe its behavior under homological projective duality. In…

We determine the algebraic and transcendental lattices of a general cubic fourfold with a symplectic automorphism of prime order. We prove that cubic fourfolds admitting a symplectic automorphism of order at least three are rational, and we…

We give a more detailed description of the new system of Pl\"ucker-like equations from [4], discuss how it relates to the usual Pl\"ucker equations, and correct a mistake in that article.

We investigate the pseudo-hyperk\"ahler geometry of higher degree rational curves in the twistor space of a hyperk\"ahler $4$-manifold.

We obtain some new inequalities of Chebyshev Type.

We give explicit descriptions of some Noether-Lefschetz divisors in the moduli space of Gushel-Mukai fourfolds. As a consequence we obtain that their Kodaira dimension is negative.

We study rationality properties of quadric surface bundles over the projective plane. We exhibit families of smooth projective complex fourfolds of this type over connected bases, containing both rational and non-rational fibers.

In this paper we determine a complete list of rational surface singularities which have metrically conical bilipschitz type of its inner metric. We achieve this by using the thick-thin decomposition of Birbrair, Neumann and Pichon.

In this short note we try to generalize the Clemens-Griffiths criterion of non-rationality for smooth cubic threefolds to the case of smooth cubic fourfolds.

In this paper, a geometric interpretation is provided of a new rational Landen transformation. The convergence of its iterates is also established.

We provide new examples of integrable rational maps in four dimensions with two rational invariants, which have unexpected geometric properties, as for example orbits confined to non algebraic varieties, and fall outside classes studied by…

We give an elementary proof of a recent result by Fishman, Kleinbock, Merrill and Simmons about rational points on quadratic surfaces.

We construct examples of nodal quartic double solids that admit uniformly rational, and so elliptic in Gromov' sense, small algebraic resolutions.

We exhibit families of smooth projective threefolds with both stably rational and non stably rational fibers.

We give in this article necessary and sufficient conditions on the topology of rationally and polynomially convex domains.

We prove that the rational blowdown, a surgery on smooth 4-manifolds introduced by Fintushel and Stern, can be performed in the symplectic category. As a consequence, interesting families of smooth 4-manifolds, including the exotic $K3$…

Recently, the non-linear Changhee differential equations were introduced in [5] and these differential equations turned out to be very useful for studying special polynomials and mathematical physics. Some interesting identities and…

We review recent progress in constructing maximal, classical supergravity models and their applications.

We construct two examples of projective hyper-K\"ahler fourfolds of K3[2]-type with an action of the alternating group A7, making them some of the most symmetric hyper-K\"ahler fourfolds. They are realized as so called double EPW sextics…