Endomorphisms of superelliptic jacobians

Let K be a field of characteristic zero, n ≥ 5 an integer, f(x) an irreducible polynomial over K of degree n, whose Galois group contains a doubly transitive simple non-abelian group. Let p be an odd prime, the ring of integers in the pth cyclotomic field, C _{f, p} : y ^p  =  f(x) the corresponding superelliptic curve and J(C _{f, p} ) its jacobian. Assuming that either n  =  p + 1 or p does not divide n(n  −  1), we prove that the ring of all endomorphisms of J(C _{f, p} ) coincides with . The same is true if n  =  4, the Galois group of f(x) is the full symmetric group S ₄ and K contains a primitive pth root of unity. An erratum to this article can be found at     

Corrigenda to “Barth type vanishing theorems”

We fix a mistake contained in a previous paper concerning vanishing theorems for low codimensional varieties in . This work is within the framework of the national research project “Geomety on Algebraic Varieties” Cofin 2008 of MIUR.     

玉米近红外光谱在仿生模式识别中的特征提取方法研究

近红外光谱特征提取是近红外光谱定性分析的关键步骤,其质量直接影响定性分析结果。采用漫透射方法测量8个玉米品种的近红外光谱,经预处理后,分别采用PCA,ICA,PLS-DA和小波分解四种方法对光谱进行特征提取,并使用仿生模式识别方法建立了8个玉米品种识别模型,最后使用测试集数据进行模型测试。结论如下:使用PLS-DA方法进行特征提取后建立的模型正确识别率优于使用PCA,ICA和小波分解特征提取后建立的模型。     

ICP-OES测定马蔺不同部位中的21种元素

采用微波消解-电感耦合等离子体-发射光谱法(ICP-OES)测定了中药材马蔺不同部位中Ca,Mg,Fe,Zn,Cu等21种元素的含量。结果表明,各元素线性关系良好,相关系数r≥0.9980;加标回收率在96.4%—103.1%之间,RSD<4.70%。马蔺的根、种子和叶中含量最多的3种元素的排序均为Ca>Mg>Fe。不同部位相较而言,元素Cr,Zn,Cu,Tl,Sb和Cd在种子中含量最多;Ca,Mg,Sr,Ni,Mo,Li和Pb在叶中含量最多;Fe,Mn,V和Ti则在根中含量最高,Co元素只在根中检出。实验结果可为马蔺中所含元素与其药效之间的关系提供一定的科学依据。     

Higher dimensional Shimura varieties in the Prym loci of ramified double covers

In this paper, we construct Shimura subvarieties of dimension bigger than one of the moduli space ${\mathsf{A}}_p^{\delta }$ of δ-polarized abelian varieties of dimension p, which are generically contained in the Prym loci of (ramified) double covers. The idea is to adapt the techniques already used to construct Shimura curves in the Prym loci to the higher dimensional case, namely, to use families of Galois covers of ${\mathbb{P}}^1$. The case of abelian covers is treated in detail, since in this case, it is possible to make explicit computations that allow to verify a sufficient condition for such a family to yield a Shimura subvariety of ${\mathsf{A}}_p^{\delta }$.     

Stability conditions on Kuznetsov components of Gushel–Mukai threefolds and Serre functor

We show that the stability conditions on the Kuznetsov component of a Gushel–Mukai threefold, constructed by Bayer, Lahoz, Macrì and Stellari, are preserved by the Serre functor, up to the action of the universal cover of ${\text{GL}}_2^{+}(\mathbb{R})$. As application, we construct stability conditions on the Kuznetsov component of special Gushel–Mukai fourfolds.