170,354 research outputs found
Linear stability for line bundles over curves
No full textLet C be a smooth irreducible projective curve and let (L, H^0(L))
be a complete and globally generated linear series on C. Denote by M_L the
syzygy bundle, kernel of the evaluation map H^0(L) ⊗ O_C → L. In this work
we restrict our attention to the case of globally generated line bundles L over a
curve with h0(L) = 3.
The purpose of this short note is to connect Mistretta-Stoppino Conjecture
on the equivalence between linear (semi)stability of L and
slope (semi)stability of M_L with the existence of extensions of line bundles
of L by certain quotients Q of M_L.
Also, we give numerical conditions to
produce examples of line bundles L which are linearly semistables but with
syzygy bundle M_L unstable, that is, we find numerical conditions to look for
counter-examples to Mistretta-Stoppino Conjecture of rank 2
On Stability of Tautological Bundles and their Total Transforms
No full textThrough the use of linearized bundles, we prove the stability of tautological bundles over the symmetric product of a curve and of the kernel of the evaluation map on their global sections
BINGE DRINKING: CONSUMPTION PRACTICES AMONG YOUNG PEOPLE. ANALYSIS OF THE QUESTIONNAIRES COMPILED BY STUDENTS OF PALERMO CITY AND PROVINCE INVOLVED IN THE PREVENTION AND INFORMATION PROJECT
No full textThe term binge drinking is used in the northern countries of Europe, to point out the consumption of great intoxicating quantities of alcohol, until feel bad, for the pure and simple desire to get drunk. Conventionally, binge drinking is the consumption
of at least six glasses of alcoholic drinks, different
ones as well, in a single occasion and one after the other. A
survey has been conducted through administration of questionnaires
with the purpose to have an idea about the territorial diffusion
of such practice among the students of Palermo and province. In the months of April and May 2014, this survey
affected 30 classes of different schools in 10 cities and
province, involving about 740 students. The number of the students
was inferable from the questionnaires compiled before the formative action. The sample results representative enough among teenagers (14/18 y.o.), and the female part is predominant.
36% declared to spend Saturday night in pubs, while 18% in discotheques. 25% of consulted people replied to connect the time spent in pubs to alcohol. Other important factors
are: 36% abuse of alcohol just in the week-end (factor confirming
the alarming Binge practice); 30% declare to get in the car
with a bit drunk driver (13% with a totally drunk driver). 65%
declare to have an adequate knowledge of potential alcohol
effects. The question about motivations convincing a teenager
to take drugs gave the following result: 40% desire of transgression;
30% desire to conform with the group; 23% the research of an easy wellness. This data convince more and
more to understand the importance of the prevention and information
role. All this to avoid that trends and lifestyles sacrifice
teenagers for the enormous economic interests staying behind
the sale of alcohol, and prepare as society more and more
salve of consumption and abuses even lethal such as alcohol
Holomorphic symmetric differentials and a birational characterization of Abelian Varieties
No full textA generically generated vector bundle on a smooth projective variety yields a rational map to a Grassmannian, called Kodaira map. We answer a previous question, raised by the asymptotic behaviour of such maps, giving rise to a birational characterization of abelian varieties. In particular we prove that, under the conjectures of the Minimal Model Program, a smooth projective variety is birational to an abelian variety if and only if it has Kodaira dimension 0 and some symmetric power of its cotangent sheaf is generically generated by its global sections
Iitaka Fibrations for Vector Bundles
No full textA vector bundle on a smooth projective variety, if it is generically generated by global
sections, yields a rational map to a Grassmannian, called Kodaira map. We investigate
the asymptotic behavior of the Kodaira maps for the symmetric powers of a vector
bundle, and we show that these maps stabilize to a map dominating all of them, as it
happens for a line bundle via the Iitka fibration. Through this Iitaka-type construction,
applied to the cotangent bundle, we give a new characterization of Abelian varieties
On linear stability and syzygy stability
No full textIn previous works, the authors investigated the relationships between linear stability of a generated linear series |V| on a curve C, and slope stability of the syzygy vector bundle MV OC → L) . In particular, the second named author and L. Stoppino conjecture that, for a complete linear system |L|, linear (semi)stability is equivalent to slope (semi)stability of ML . The first and third named authors proved that this conjecture holds in the two opposite cases: hyperelliptic and generic curves. In this work we provide a counterexample to this conjecture on any smooth plane curve of degree 7
On semiample vector bundles and parallelizable compact complex manifolds
No full textWe provide a characterization of parallelizable compact complex manifolds and their quotients using holomorphic symmetric differentials. In particular we show that compact complex manifolds of Kodaira dimension 0 having strongly semiample cotangent bundle are parallelizable manifolds, while compact complex manifolds of Kodaira dimension 0 having weakly semiample cotangent bundle are quotients of parallelizable manifolds. The main constructions used involve considerations about semiampleness of vector bundles, which are themselves of interest. As a byproduct we prove that compact manifolds having Kodaira dimension 0 and weakly sermiample cotangent bundle have infinite fundamental group, and we conjecture that this should be the case for all compact complex manifolds not of general type with weakly semiample cotangent bundle
Linear series on curves: stability and Clifford index
No full textWe study concepts of stabilities associated to a smooth complex curve
together with a linear series on it. In particular we investigate the relation
between stability of the associated Dual Span Bundle and linear stability. Our
result implies a stability condition related to the Clifford index of the
curve. Furthermore, in some of the cases, we prove that a stronger stability
holds: cohomological stability. Eventually using our results we obtain stable
vector bundles of integral slope 3, and prove that they admit theta-divisors.Comment: 24 page
Standard isotrivial fibrations with p(g) = q=1, II
No full textA smooth, projective surface S is called a standard isotrivial fibration if there exists a finite group G which acts faithfully on two smooth projective curves C and F so that S is isomorphic to the minimal desingularization of T := (C × F )/G.
Standard isotrivial fibrations of general type with pg = q = 1 have been classified in
[F. Polizzi, Standard isotrivial fibrations with pg = q = 1, J. Algebra 321 (2009),1600–1631]
under the assumption that T has only Rational Double Points as singularities.
In the present paper we extend this result, classifying all cases where S is a minimal model.
As a by-product, we provide the first examples of minimal surfaces of general type with pg = q = 1, K^2 = 5 and Albanese fibration of genus 3.
Finally, we show with explicit examples that the case where S is not minimal actually occurs
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