The main results of this article are asymptotic formulas for the variance of the number of zeros of a Gaussian random polynomial of degree N in an open set U ⊂ C as the degree N → ∞, and more generally for the zeros of random holomorphic sections of high powers of any positive line bundle over any Riemann surface. The formulas were conjectured in special cases by Forrester and Honner. In higher...

Our molecular simulations reveal that wild-type influenza fusion peptides are able to stabilize a highly fusogenic pre-fusion structure, i.e. a peptide bundle formed by four or more trans-membrane arranged fusion peptides. We rationalize that the lipid rim around such bundle has a non-vanishing rim energy (line-tension), which is essential to (i) stabilize the initial contact point between the ...

We give the first examples of nef line bundles on smooth projective varieties over finite fields which are not semi-ample. More concretely, we find smooth curves on smooth projective surfaces over finite fields such that the normal bundle has degree zero, but no positive multiple of the curve moves in a family of disjoint curves. This answers questions by Keel and Mumford. The proof uses an obs...

In this paper we apply Arakelov theory to study the distribution of Petersson norms classical cusp forms as well sup rational functions on adelic subsets curves. The method in both cases is limiting successive minima global sections powers a metrized ample line bundle one takes increasing bundle. We develop general for computing measure associated distribution. also measures zeros which have sm...

In this paper we review the concepts of the superalgebra, superderivation and some properties of them. We will define algebraic and differential superderivations on a superalgebra and will prove some theorems about them, Then we consider a superalgebra bundle, that is an algebra bundle which its fibers are superalgebras and then characterize the superderivations of the algebra of sections of th...

Smooth complex surfaces polarized with an ample and globally generated line bundle of degree three and four, such that the adjoint bundle is not globally generated, are considered. Scrolls of a vector bundle over a smooth curve are shown to be the only examples in degree three. Two classes of examples in degree four are presented, one of which is shown to characterize regular such pairs. A Reid...

Let M be a compact connected Fujiki manifold, G semisimple affine algebraic group over C with one simple factor and P fixed proper parabolic subgroup of G. For holomorphic principal G–bundle EG M, let EP the P–bundle EG⟶EG/P given by quotient map. We prove that following three statements are equivalent: (1) ad(EG) is numerically flat, (2) line bundle ⋀topad(EP)⁎ nef, (3) for every reduced irred...

Central line-associated bloodstream infection (CLABSIs) is an important healthcare-associated infection in the critical care units. It causes substantial morbidity, mortality and incurs high costs. The use of central venous line (CVL) insertion bundle has been shown to decrease the incidence of CLABSIs. Our aim was to study the impact of CVL insertion bundle on incidence of CLABSI and study the...

Recent work of Kass–Wickelgren gives an enriched count the 27 lines on a smooth cubic surface over arbitrary fields. Their approach using $$\mathbb {A}^1$$ -enumerative geometry suggests that other classical enumerative problems should have similar enrichments, when answer is computed as degree Euler class relatively orientable vector bundle. Here, we consider closely related problem 28 bitange...

For a vector bundle E of rank n + 1 over a smooth projective curve C of genus g, let X = PC(E) with projection map π : X → C. In this paper we investigate the minimal free resolution of homogeneous coordinate rings of X . We first clarify the relations between higher syzygies of very ample line bundles on X and higher syzygies of Veronese embedding of fibres of π by the same line bundle. More p...