Search results for "varieties"

Voisin's Conjecture for 0-cycles on Calabi-Yau varieties and their mirror

2019

We study a conjecture, due to Voisin, on 0-cycles on varieties with pg = 1. Using Kimura’s finite dimensional motives and recent results of Vial’s on the refined (Chow–)Künneth decomposition, we provide a general criterion for Calabi–Yau manifolds of dimension at most 5 to verify Voisin’s conjecture. We then check, using in most cases some cohomological computations on the mirror partners, that the criterion can be successfully applied to various examples in each dimension up to 5.

Correspondence between some metabelian varieties and left nilpotent varieties

2021

Abstract In the class of left nilpotent algebras of index two it was proved that there are no varieties of fractional polynomial growth ≈ n α with 1 α 2 and 2 α 3 instead it was established the existence of a variety of fractional polynomial growth with α = 7 2 . In this paper we investigate similar problems for varieties of commutative or anticommutative metabelian algebras. We construct a correspondence between left nilpotent algebras of index two and commutative metabelian algebras or anticommutative metabelian algebras and we prove that the codimensions sequences of the corresponding algebras coincide up to a constant. This allows us to transfer the above results concerning varieties of…

The Coble Quadric

2023

Given a smooth genus three curve $C$, the moduli space of rank two stable vector bundles on C with trivial determinant embeds in $\mathbb{P}^8$ as a hypersurface whose singular locus is the Kummer threefold of $C$; this hypersurface is the Coble quartic. Gruson, Sam and Weyman realized that this quartic could be constructed from a general skew-symmetric fourform in eight variables. Using the lines contained in the quartic, we prove that a similar construction allows to recover SU$_C(2, L)$, the moduli space of rank two stable vector bundles on C with fixed determinant of odd degree L, as a subvariety of $G(2, 8)$. In fact, each point $p \in C$ defines a natural embedding of SU$_C(2, \mathca…

Varieties with at most quadratic growth

2010

Let V be a variety of non necessarily associative algebras over a field of characteristic zero. The growth of V is determined by the asymptotic behavior of the sequence of codimensions cn(V); n = 1; 2, … and here we study varieties of polynomial growth. Recently, for any real number a, 3 < a < 4, a variety V was constructed satisfying C1n^a < cn(V) < C2n^a; for some constants C1;C2. Motivated by this result here we try to classify all possible growth of varieties V such that cn(V) < Cn^a; with 0 < a < 2, for some constant C. We prove that if 0 < a < 1 then, for n large, cn(V) ≤ 1, whereas if V is a commutative variety and 1 < a < 2, then lim logn cn(V) = 1 o…

Abelian gradings on upper-triangular matrices

2003

Let G be an arbitrary finite abelian group. We describe all possible G-gradings on an upper-triangular matrix algebra over an algebraically closed field of characteristic zero.

Valutazione dell’Abilità Competitiva nei Confronti delle Malerbe di Genotipi Antichi e Moderni di Frumento Duro.

2013

Hybrid bases for varieties of semigroups

2003

We consider the lower part of the lattice of varieties of semigroups. We present finite bases of hybrid identities for the varieties of normal bands, commutative bands and abelian groups of finite exponent. The variety A n,0 of abelian groups provides an example of a variety which has no finite base of hyperidentities (cf. [12]) but has a finite base of hybrid identities.

Triple planes with $p_g=q=0$

2019

We show that general triple planes with p_g=q=0 belong to at most 12 families, that we call surfaces of type I,..., XII, and we prove that the corresponding Tschirnhausen bundle is direct sum of two line bundles in cases I, II, III, whereas is a rank 2 Steiner bundle in the remaining cases. We also provide existence results and explicit constructions for surfaces of type I,..., VII, recovering all classical examples and discovering several new ones. In particular, triple planes of type VII provide counterexamples to a wrong claim made in 1942 by Bronowski.

Le varietà di grano duro per le semine 2021. Sicilia

2021

Anche nel 2020-21, pur nelle difficili circostanze determinate per il secondo anno consecutivo dalla pandemia da Covid-19, sono state condotte in Sicilia le prove della Rete nazionale di confronto varietale di frumento duro. I campi sperimentali sono stati allestiti in 5 ambienti siciliani. La sperimentazione ha riguardato 30 varieta’, di cui ben 9 al primo anno di valutazione. I risultati produttivi riscontrati nelle diverse localita’ appaiono molto differenti e fortemente influenzati dall’andamento meteorologico verificatosi nelle diverse zone dell’Isola. At 2020-21, despite the difficult circumstances determined for the second consecutive year by the Covid-19 pandemic, the tests of the n…

Le varietà di grano duro per le semine 2020: Sicilia

2020

Nonostante le difficoltà operative dovute alla pandemia da Covid-19, anche nel corso del 2019-20 sono state condotte in Sicilia le prove di confronto varietale di frumento duro, allestite in 5 località della Sicilia: Libertinia (Catania), Catania, S. Stefano Quisquina (Agrigento), Caltagirone (Catania) e Ciminna (Palermo). La sperimentazione ha riguardato 30 varietà, di cui 5 al primo anno di valutazione, 9 cultivar al secondo anno di prova e 16 genotipi testati da oltre due anni. La resa media dell’areale siciliano è stata pari a 6,11 t/ha e i risultati produttivi registrati nei diversi ambienti di prova appaiono sensibilmente influenzati dall’andamento termo-pluviometrico. Despite the dif…