Related papers: Some new rational Gushel fourfolds
The moduli spaces of trigonal curves of odd genus $g>4$ are proven to be rational.
We exhibit explicit examples of very general special cubic fourfolds with discriminant $d$ admitting an associated (twisted) K3 surface, which have non-isomorphic Fourier-Mukai partners. In particular, in the untwisted setting, we show that…
We present new computational methods for proving diffeomorphy of triangulated 4-manifolds, including algorithms and topological software that can for the first time effectively handle the complexities that arise in dimension four and be…
We formulate a conjecture on the finitude of rationality fields (i.e., Fourier coefficient fields) of newforms of bounded degree, and prove this for CM forms assuming a generalized Riemann hypothesis. Then we explicitly determine what…
We use a generalised Kummer construction to realise all but one known weight four newforms with complex multiplication and rational Fourier coefficients in smooth Calabi-Yau threefolds defined over the rational numbers. The Calabi-Yau…
An ordinary Gushel-Mukai variety with a single isolated node is the intersection of the Grassmannian $G(2,5)$ with a nodal quadric and a linear space. We consider such intersections in dimension three, four and five. We describe a flop…
We study L-equivalence in the Grothendieck ring of varieties and its interaction with categorical invariants of cubic fourfolds. Assuming a Derived Torelli-type criterion for Kuznetsov components and a mild condition on the discriminant of…
In this article we present a new method to obtain polynomial lower bounds for Galois orbits of torsion points of one dimensional group varieties.
We present some new linear, quadratic, cubic and quartic binomial Fibonacci, Lucas and Fibonacci--Lucas summation identities.
Computations in renormalizable perturbative quantum field theories reveal mathematical structures which go way beyond the formal structure which is usually taken as underlying quantum field theory. We review these new structures and the…
We study algebraic cycles on complex Gushel-Mukai (GM) varieties. We prove the generalised Hodge conjecture, the (motivated) Mumford-Tate conjecture, and the generalised Tate conjecture for all GM varieties. We compute all integral Chow…
This article investigates a new gauge theoretic approach to Einstein's equations in dimension 4. Whilst aspects of the formalism are already explained in various places in the mathematics and physics literature, our first goal is to give a…
In this paper, we consider the new q-extension of Frobenius-Euler numbers and polynomials and we derive some interesting identities from the orthogonality type properties for the new q-extension of Frobenius-Euler polynomials. Finally we…
We prove the potential density of rational points on the variety of lines of a sufficiently general cubic fourfold defined over a number field, where ``sufficiently general'' means that a condition of Terasoma type is satisfied. These…
We give new, explicit and asymptotically sharp, lower bounds for dimensions of irreducible modular representations of finite symmetric groups.
In this paper, we investigate a novel form of approximate orthogonality that is based on integral orthogonality. Additionally, we establish the fundamental properties of this new approximate orthogonality and examine its capability to…
We survey our recent new results on the geometry of Teichmuller and moduli spaces of Riemann surfaces and Calabi-Yau manifolds.
We study the degree of the special cubic fourfolds in the Hilbert scheme of cubic fourfolds via a computation of the generating series of Heegner divisors of even lattice of signature (2, 20).
We determine the group of all Fourier-Mukai type autoequivalences of Kuznetsov components of smooth complex cubic threefolds, and provide yet another proof for the Fourier-Mukai version of categorical Torelli theorem for smooth complex…
We study degree two unirational parameterizations of geometrically rational surfaces over the real field.