Annali dell''Universita di Ferrara最新文献

We investigate the rationality problem for ({mathbb {Q}})-Fano threefolds of Fano index (ge 2).

By recursively applying the prime decomposition to the exponents, every natural number determines a rooted planar tree in a canonical way. In particular, trees with only one edge correspond to prime numbers. In this work we investigate the occurrence and the distribution of patterns of trees associated to the natural numbers. Bounds from above and below are proven for certain natural quantities. It is proved that the distance between two consecutive occurrences of the same configuration of trees is unbounded. For any k, there is at least one configuration of trees arising from k consecutive integers that occurs infinitely many times. Dirichlet theorem about primes in arithmetic progressions is generalized to any planar rooted tree. The appearence of equal nonplanar trees associated to k consecutive integers is also investigated. Finally, constraints implied by the repeated occurrence of a given configuration of planar trees are analyzed.

In this note, we study K-stability of smooth Fano threefolds that can be obtained by blowing up the three-dimensional projective space along a smooth elliptic curve of degree five.

We prove that all general smooth Fano threefolds of Picard rank 3 and degree 14 are K-stable, where the generality condition is stated explicitly.

Suppose ({mathcal {R}}) is a prime ring with characteristic other than two and (nu (s_1,ldots , s_n)) is a non-central multilinear polynomial over ({mathcal {C}}), which is non-identity. If ({mathcal {H}}_1) and ({mathcal {H}}_2) are two generalized skew derivations on the ring ({mathcal {R}}), satisfying the equation

for all (s = (s_1, ldots , s_n) in {mathcal {R}}^n.) Then, we provide a comprehensive analysis of the mappings ( {mathcal {H}}_1) and ({mathcal {H}}_2) outlining their complete structure.

This is a revised version of the lecture notes prepared for the workshop on “Plane quartics, Scorza map and related topics”, held in Catania, January 19–21, 2016. The last section contains eight Macaulay2 scripts on theta characteristics and the Scorza map, with a tutorial. The first sections give an introduction to these scripts. The tutorial contains a list of the 36 Scorza preimages of the Edge quartic.

We describe the automorphism groups of smooth Fano threefolds of rank 2 and degree 28 in the cases where they are finite.

Let R be a commutative ring with identity 1. Then the graph of R, denoted by (G_P(R)) which is defined as the vertices are the elements of R and any two distinct elements a and b are adjacent if and only if the corresponding principal ideals aR and bR satisfy the condition: ((aR)(bR)=aRbigcap bR). In this paper, we characterize the class of finite commutative rings with 1 for which the graph (G_P(R)) is complete. Here we are able to show that the graph (G_P(R)) is a line graph of some graph G if and only if (G_P(R)) is complete. For (n=p_1^{r_1}p_2^{r_2}ldots p_{k}^{r_k}), we show that chromatic number of (G_P(mathbb {Z}_n)) is equal to the sum of the number of regular elements in (mathbb {Z}_n) and the number of integers i such that ({r_{i}}>1). Moreover, we characterize those n for which the graph (G_P(mathbb {Z}_n)) is end-regular.

We study factorizations of HOMFLY polynomials of certain prime knots and oriented links. We begin with a computer analysis of prime knots with at most 12 crossings, finding 17 non-trivial factorizations. Next, we give an irreducibility criterion for HOMFLY polynomials of oriented links associated to 2-connected plane graphs.