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We prove that on a general hypersurface in $\mathbb{P}^N$ of degree $d$ and dimension at least $2$, if an arithmetically Cohen-Macaulay (ACM) bundle $E$ and its dual have small regularity, then any non-trivial Hodge class in $H^{n}(X, E\otimes\Omega^n_X)$, $n = \lfloor\frac{N-1}{2}\rfloor$, produces a trivial direct summand of $E$. As a consequence, we prove that there is no universal Ulrich bundle on the family of smooth hypersurfaces of degree $d\geq 3$ and dimension at least $4$. This last statement may be viewed as a Franchetta-type conjecture for Ulrich bundles on smooth hypersurfaces., Comment: 16 pages, final version, Annali della Scuola Normale Superiore di Pisa, Classe di Scienze (to appear)

Superlattices consist of two ferromagnets La0.7Sr0.3MnO3(LSMO)and SrRuO3(SRO) were grown in (110)-orientation on SrTiO3(STO) substrates. The x-ray diffraction and Raman spectra of these superlattices show the presence of in-plane compressive strain and orthorhombic structure of less than 4 u.c. thick LSMO spacer,respectively. Magnetic measurements reveal several features including reduced magnetization, enhanced coercivity, antiferromagnetic coupling, and switching from antiferromagnetic to ferromagnetic coupling with magnetic field orientations. These magnetic properties are explained by the observed orthorhombic structure of spacer LSMO in Raman scattering which occurs due to the modification in the stereochemistry of Mn at the interfaces of SRO and LSMO.

Electronic structure and optical band gap of CoFe2O4 thin films grown on (001) oriented LaAlO3 have been investigated. Surprisingly, these films show additional Raman modes at room temperature as compared to a bulk spinel structure. The splitting of Raman modes is explained by considering the short-range ordering of Co and Fe cations in octahedral site of spinel structure. In addition, an expansion of band-gap is observed with the reduction of film thickness, which is explained by the quantum size effect and misfit dislocation. Such results provide interesting insights for the growth of spinel phases., Comment: 15 pages, 5 figures, and 1 table; Accepted and to be published/appeared in APL soon

Recently it has been proved that any arithmetically Cohen-Macaulay (ACM) bundle of rank two on a general, smooth hypersurface of degree at least three and dimension at least four is a sum of line bundles. When the dimension of the hypersurface is three, a similar result is true provided the degree of the hypersurface is at least six. We extend these results to complete intersection subvarieties by proving that any ACM bundle of rank two on a general, smooth complete intersection subvariety of sufficiently high multi-degree and dimension at least four splits. We also obtain partial results in the case of threefolds., Comment: 15 pages

We show that for a smooth hypersurface $X\subset \bbP^n$ of degree at least 2, there exist arithmetically Cohen-Macaulay (ACM) codimension two subvarieties $Y\subset X$ which are not an intersection $X\cap{S}$ for a codimension two subvariety $S\subset\bbP^n$. We also show there exist $Y\subset X$ as above for which the normal bundle sequence for the inclusion $Y\subset X\subset\bbP^n$ does not split., Comment: 8 pages

We prove that any arithmetically Gorenstein curve on a smooth, general hypersurface $X\subset \bbP^{4}$ of degree at least 6, is a complete intersection. This gives a characterisation of complete intersection curves on general type hypersurfaces in $\bbP^4$. We also verify that certain 1-cycles on a general quintic hypersurface are non-trivial elements of the Griffiths group., Comment: 14 pages

We study certain moduli spaces of stable vector bundles of rank two on cubic and quartic threefolds. In many cases under consideration, it turns out that the moduli space is complete and irreducible and a general member has vanishing intermediate cohomology. In one case, all except one component of the moduli space has such vector bundles., Comment: 12 pages, Journal of Pure and Applied Algebra (to appear)

We prove that any rank two arithmetically Cohen-Macaulay vector bundle on a general hypersurface of degree at least six in projective four space must be split., Comment: 10 pages, Submitted version

Let $k$ be a field of arbitrary characteristic. Let $S$ be a singular surface defined over $k$ with multiple rational curve singularities and suppose that the Chow group of zero cycles of its normalisation $\tilde{S}$ is finite dimensional. We give numerical conditions under which the Chow group of zero cycles of $S$ is finite dimensional., Comment: 14 pages

We prove that for a normal projective variety $X$ in characteristic 0, and a base-point free ample line bundle $L$ on it, the restriction map of divisor class groups $\Cl(X)\to \Cl(Y)$ is an isomorphism for a general member $Y\in |L|$ provided that $\dim{X}\geq 4$. This is a generalization of the Grothendieck-Lefschetz Theorem, for divisor class groups of singular varieties., Comment: 21 pages, no figures, to appear in J. Algebraic Geometry

We prove that any rank two arithmetically Cohen-Macaulay vector bundle on a general hypersurface of degree at least three in $\mathbb{P}^5$ must be split., Comment: 14 pages

This paper forms the major portion of a talk given at the International Colloquium on Arithmetic, Algebra and Geometry at TIFR, Mumbai in Jan 2000. We look at the problem of detecting cycles with trivial Abel-Jacobi invariant. M. Green proposed a Hodge-theoretic method to which C. Voisin found a counter-example. We present an easier example. We also propose another possible invariant to detect these classes using Hodge Theory. Similar methods have been proposed earlier by M. Asakura and M. Saito., Comment: amslatex (amsart 1997/03/26 v1.2r); 8 pages