Search results for "BVAR"
showing 6 items of 16 documents
The generic local structure of time-optimal synthesis with a target of codimension one in dimension greater than two
1997
In previous papers, we gave in dimension 2 and 3 a classification of generic synthesis of analytic systems\(\dot v(t) = X(v(t)) + u(t)Y(v(t))\) with a terminal submanifoldN of codimension one when the trajectories are not tangent toN. We complete here this classification in all generic cases in dimension 3, giving a topological classification and a model in each case. We prove also that in dimensionn≥3, out of a subvariety ofN of codimension there, we have described all the local synthesis.
On the Oort conjecture for Shimura varieties of unitary and orthogonal types
2014
In this paper we study the Oort conjecture on Shimura subvarieties contained generically in the Torelli locus in the Siegel modular variety $\mathcal{A}_g$. Using the poly-stability of Higgs bundles on curves and the slope inequality of Xiao on fibred surfaces, we show that a Shimura curve $C$ is not contained generically in the Torelli locus if its canonical Higgs bundles contains a unitary Higgs subbundle of rank at least $(4g+2)/5$. From this we prove that a Shimura subvariety of $\mathbf{SU}(n,1)$-type is not contained generically in the Torelli locus when a numerical inequality holds, which involves the genus $g$, the dimension $n+1$, the degree $2d$ of CM field of the Hermitian space,…
Deformations of Calabi-Yau manifolds in Fano toric varieties
2020
In this article, we investigate deformations of a Calabi-Yau manifold $Z$ in a toric variety $F$, possibly not smooth. In particular, we prove that the forgetful morphism from the Hilbert functor $H^F_Z$ of infinitesimal deformations of $Z$ in $F$ to the functor of infinitesimal deformations of $Z$ is smooth. This implies the smoothness of $H^F_Z $ at the corresponding point in the Hilbert scheme. Moreover, we give some examples and include some computations on the Hodge numbers of Calabi-Yau manifolds in Fano toric varieties.
An uncountable family of almost nilpotent varieties of polynomial growth
2017
A non-nilpotent variety of algebras is almost nilpotent if any proper subvariety is nilpotent. Let the base field be of characteristic zero. It has been shown that for associative or Lie algebras only one such variety exists. Here we present infinite families of such varieties. More precisely we shall prove the existence of 1) a countable family of almost nilpotent varieties of at most linear growth and 2) an uncountable family of almost nilpotent varieties of at most quadratic growth.
Hurwitz spaces of quadruple coverings of elliptic curves and the moduli space of abelian threefolds A_3(1,1,4)
2005
We prove that the moduli space A_3(1,1,4) of polarized abelian threefolds with polarization of type (1,1,4) is unirational. By a result of Birkenhake and Lange this implies the unirationality of the isomorphic moduli space A_3(1,4,4). The result is based on the study the Hurwitz space H_{4,n}(Y) of quadruple coverings of an elliptic curve Y simply branched in n points. We prove the unirationality of its codimension one subvariety H^{0}_{4,A}(Y) which parametrizes quadruple coverings ��:X --> Y with Tschirnhausen modules isomorphic to A^{-1}, where A\in Pic^{n/2}Y, and for which ��^*:J(Y)--> J(X) is injective. This is an analog of the result of Arbarello and Cornalba that the Hurwitz s…
Stabilization of the cohomology of thickenings
2016
For a local complete intersection subvariety $X=V({\mathcal I})$ in ${\mathbb P}^n$ over a field of characteristic zero, we show that, in cohomological degrees smaller than the codimension of the singular locus of $X$, the cohomology of vector bundles on the formal completion of ${\mathbb P}^n$ along $X$ can be effectively computed as the cohomology on any sufficiently high thickening $X_t=V({\mathcal I^t})$; the main ingredient here is a positivity result for the normal bundle of $X$. Furthermore, we show that the Kodaira vanishing theorem holds for all thickenings $X_t$ in the same range of cohomological degrees; this extends the known version of Kodaira vanishing on $X$, and the main new…