Related papers: Fano's inequality is also false for three-dimensio…

A bilinear inequality of Geba, Greenleaf, Iosevich, Palsson, and Sawyer for the Fourier transform is shown to be equivalent to a simpler linear inequality, and the range of exponents is extended. Related mixed-norm inequalities are…

Let $X$ be a cubic fourfold that has only simple singularities and does not contain a plane. We prove that the Fano variety of lines on $X$ has the same analytic type of singularity as the Hilbert scheme of two points on a surface with only…

The F theorem states that, for a unitary three dimensional quantum field theory, the F quantity defined in terms of the partition function on a three sphere is positive, stationary at fixed point and decreases monotonically along a…

We present a smooth, complete toric threefold with no nontrivial nef line bundles. This is a counterexample to a recent conjecture of Fujino.

A $q$-analogue of a $t$-design is a set $S$ of subspaces (of dimension $k$) of a finite vector space $V$ over a field of order $q$ such that each $t$ subspace is contained in a constant $\lambda$ number of elements of $S$. The smallest…

Four classes of three dimensional quadratic algebras of the type $\lsb Q_0 , Q_\pm \rsb$ $=$ $\pm Q_\pm$, $\lsb Q_+ , Q_- \rsb$ $=$ $aQ_0^2 + bQ_0 + c$, where $(a,b,c)$ are constants or central elements of the algebra, are constructed using…

An inequality concerning ratios of gamma functions is proved. This answers a question of Guo and Qi (2003).

In this article we prove some strong vanishing theorems on K3 surfaces. As an aplication of them, we obtain higher syzygy results for K3 surfaces and Fano varieties.

In a previous study, we have discovered that nonlinear processes can be enhanced several orders of magnitude due to the path interference effects which are introduced by Fano resonances. Emergence of this phenomenon has been demonstrated…

Fourier transform is applied to annular beams of simplified flat two-level geometry: bright outer ring with a darker core. The pattern of focal beam profile (i.e. far field) is calculated and characterized with respect of its intensity…

The triadic description of General Relativity in three dimensions is known to be a BF theory. Diffeomorphisms, as symmetries, are easily re- covered on shell from the symmetries of BF theory. This note describes an explicit off-shell BV…

In the present work, we will develop a conformal inequality in the hyperbolic foliation context which is analogous to the conformal inequality in the classical time-constant foliation context. Then as an application, we will apply this a…

We compute the facets of the effective cones of divisors on the blow-up of P^3 in up to five lines in general position. We prove that up to six lines these threefolds are weak Fano and hence Mori Dream Spaces.

We generalize the equivariant intermediate Jacobian torsor obstruction over $\mathbb{C}$ to algebraically closed fields of characteristic zero. It is an obstruction to the (projective) linearizability problem of finite group actions on…

Non-alternating Hamiltonian Lie algebras in three variables over a perfect field of characteristic 2 are considered. A classification of non-alternating Hamiltonian forms over an algebra of divided powers in three variables and of the…

In a photoionization spectrum in which there is no excitation of the discrete states, but only the underlying continuum, we have observed resonances which appear as symmetric peaks, not the commonly expected window resonances. Furthermore,…

A powerful tool of investigation of Fano varieties is provided by exceptional collections in their derived categories. Proving the fullness of such a collection is generally a nontrvial problem, usually solved on a case-by-case basis, with…

We show that the presence of a side-attached state strongly modifies the transmission through a one-dimensional double-barrier system in the window of wavevectors around the Fano antiresonance. Specifically, the interplay between the Fano…

For a positive integer $n$, an $n$-sided polygon lying on a circular arc or, shortly, an $n$-fan is a sequence of $n+1$ points on a circle going counterclockwise such that the "total rotation" $\delta$ from the first point to the last one…

This paper studies the defect of terminal Gorenstein Fano 3 folds. I determine a bound on the defect of terminal Gorenstein Fano 3-folds of Picard rank 1 that do not contain a plane. I give a general bound for quartic 3-folds and indicate…