361 research outputs found
Calabi-Yau quotients with terminal singularities
In this paper we are interested in quotients of Calabi-Yau threefolds with
isolated singularities. In particular, we analyze the case when has
terminal singularities. We prove that, if is cyclic of prime order and
has terminal singularities, then has order or .Comment: 15 pages, no figures. Current version has some changes in the
structure of the article, some corrected typos and an up-to-date bibliograph
Covering of elliptic curves and the kernel of the Prym map
Motivated by a conjecture of Xiao, we study families of coverings of elliptic
curves and their corresponding Prym map . More precisely, we describe the
codifferential of the period map associated to in terms of the
residue of meromorphic -forms and then we use it to give a characterization
for the coverings for which the dimension of is the least possibile.
This is useful in order to exclude the existence of non isotrivial fibrations
with maximal relative irregularity and thus also in order to give
counterexamples to the Xiao's conjecture mentioned above. The first
counterexample to the original conjecture, due to Pirola, is then analysed in
our framework.Comment: 21 pages, no figures. The seminal ideas at the base of this article
were born in the framework of the PRAGMATIC project of year 201
Underwater laboratory: Teaching physics through diving practice
Diving education and diving science and technology may be a useful tool in teaching physics in non–physics-oriented High School courses. In this paper we present an activity which combines some simple theoretical aspects of fluid statics, fluid dynamics and gas behavior under pressure with diving experience, where the swimming pool and the sea are used as a laboratory. This topic had previously been approached in a pure experimental way in school laboratory, but some particular experiments became much more attractive and meaningful to the students when they could use their bodies to perform them directly in water. The activity was carried out with groups of students from Italian High School classes in different situations
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New examples of Calabi-Yau threefolds and genus zero surfaces
We classify the subgroups of the automorphism group of the product of 4
projective lines admitting an invariant anticanonical smooth divisor on which
the action is free. As a first application, we describe new examples of
Calabi-Yau 3-folds with small Hodge numbers. In particular, the Picard number
is 1 and the number of moduli is 5. Furthermore, the fundamental group is
non-trivial. We also construct a new family of minimal surfaces of general type
with geometric genus zero, K^2=3 and fundamental group of order 16. We show
that this family dominates an irreducible component of dimension 4 of the
moduli space of the surfaces of general type.Comment: 18 pages; v2: simplified some arguments in the last section, final
version to appear on Communications in Contemporary Mathematic
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