Related papers: Four generated 4-instantons
We study a class of torsion-free sheaves on complex projective spaces which generalize the much studied mathematical instanton bundles. Instanton sheaves can be obtained as cohomologies of linear monads and are shown to be semistable if its…
An old theorem, due to Graustein, asserts that the average curvature of a plane oval is attained at least at four points. We present a proof by way of wave propagation and extend this result to the spherical and hyperbolic geometries - in…
Much of arithmetic geometry is concerned with the study of principal bundles. They occur prominently in the arithmetic of elliptic curves and, more recently, in the study of the Diophantine geometry of curves of higher genus. In particular,…
Instantons in massless theories do not carry over to massive theories due to Derrick's theorem. This theorem can, however, be circumvented, if a constraint that restricts the scale of the instanton is imposed on the theory. Constrained…
Graphons are analytic objects associated with convergent sequences of dense graphs. Finitely forcible graphons, i.e., those determined by finitely many subgraph densities, are of particular interest because of their relation to various…
In this paper we relate some classical normal forms for complex elliptic curves in terms of 4-point sets in the Riemann sphere. Our main result is an alternative proof that every elliptic curve is isomorphic as a Riemann surface to one in…
The present paper is devoted to the investigation of absolutely continuous curves in asymmetric metric spaces induced by Finsler structures. Firstly, for asymmetric spaces induced by Finsler manifolds, we show that three different kinds of…
In this largely-expository note, we describe a class of divisors on elliptic curves that index the inflection points of linear series arising (as subspaces of holomorphic sections) from line bundles on $\mathbb{P}^1$ via pullback along the…
In this paper we study a relationship between systems of $n$ subspaces and representations of $*$-algebras generated by projections. We prove that irreducible nonequivalent $*$-representations of $*$-algebras $\mathcal P_{4,com}$ generate…
We give some new explicit examples of putatively optimal projective spherical designs. i.e., ones for which there is numerical evidence that they are of minimal size. These form continuous families, and so have little apparent symmetry in…
The 'tHooft's 5N-parametric multiinstanton solution is generalized to curvilinear coordinates. Expressions can be simplified by a gauge transformation that makes $\eta$-symbols constant in the vierbein formalism. This generates the…
We develop the theory of derived differential geometry in terms of bundles of curved $L_\infty[1]$-algebras, i.e. dg manifolds of positive amplitudes. We prove the category of derived manifolds is a category of fibrant objects. Therefore,…
We derive a numerical criterion for J-holomorphic curves in 4-dimensional symplectic cobordisms to achieve transversality without any genericity assumption. This generalizes results of Hofer-Lizan-Sikorav and Ivashkovich-Shevchishin to…
Denoting by ${\mathcal L}_d(m_0,m_1,...,m_r)$ the linear system of plane curves passing through $r+1$ generic points $p_0,p_1,...,p_r$ of the projective plane with multiplicity $m_i$ (or larger) at each $p_i$, we prove the…
In this paper, we prove that $\mathbb{P}^2$ blown up at seven general points admits a conic bundle structure over $\mathbb{P}^1$ and it can be embedded as $(2,2)$ divisor in $\mathbb{P}^{1}\times\mathbb{P}^{2}$. Conversely, any smooth…
Branches of moduli space of F-theory in four dimensions are investigated. The transition between two branches is described as a 3-brane-instanton transition on a 7-brane. A dual heterotic picture of the transition is presented and the…
Universal spacetimes are exact solutions to all higher-order theories of gravity. We study these spacetimes in four dimensions and provide necessary and sufficient conditions for universality for all Petrov types except of type II. We show…
Gieseker-Nakajima moduli spaces $M_{k}(n)$ parametrize the charge $k$ noncommutative $U(n)$ instantons on ${\bf R}^{4}$ and framed rank $n$ torsion free sheaves $\mathcal{E}$ on ${\bf C\bf P}^{2}$ with ${\rm ch}_{2}({\mathcal{E}}) = k$.…
P. Ellia and G.Sacchiero have shown that if $S$ is a smooth surface in $\Pn 4$ which is ruled in conics, then $S$ has degree 4 or 5. In this paper we give a proof of this result combining the ideas of Ellia and Sacchiero as they are used in…
We give new bounds for the number of integral points on elliptic curves. The method may be said to interpolate between approaches via diophantine techniques ([BP], [HBR]) and methods based on quasiorthogonality in the Mordell-Weil lattice…