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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) → Cl(Y ) is an isomorphism for a general member Y ∈ |L| provided that dimX ≥ 4. This is a generalization of the Grothendieck-Lefschetz theorem, for divisor class groups of singular varieties.… (More)

- G. V. Ravindra
- 2008

Let X be a normal projective threefold over a field of characteristic zero and |L| be a base-point free, ample linear system on X. Under suitable hypotheses on (X, |L|), we prove that for a very general member Y ∈ |L|, the restriction map on divisor class groups Cl (X)→ Cl (Y ) is an isomorphism. In particular, we are able to recover the classical… (More)

We prove that any rank two arithmetically CohenMacaulay vector bundle on a general hypersurface of degree at least three in P must be split.

We prove that any rank two arithmetically CohenMacaulay vector bundle on a general hypersurface of degree at least six in P must be split.

Let X be a smooth projective variety over an algebraically closed field k ⊂ C of characteristic zero, and Y ⊂ X a smooth complete intersection. The Weak Lefschetz theorem states that the natural restriction map H(X(C), Q) → H(Y (C), Q) on singular cohomology is an isomorphism for all i < dim(Y ). The Bloch-Beilinson conjectures on the existence of certain… (More)

- G. V. Ravindra
- 2005

We prove that for a generic hypersurface in P of degree at least 2 + 2/n, the n-th Picard number is one. The proof is algebraic in nature and follows from certain coherent cohomology vanishing.

This paper shows that the general hypersurface of degree ≥ 6 in projective four space cannot support an indecomposable rank two vector bundle which is Arithmetically CohenMacaulay and four generated. Equivalently, the equation of the hypersurface is not the Pfaffian of a four by four minimal skewsymmetric matrix.

We prove that on a generic hypersurface in P of dimension at least 3, a vector bundle with r ≤ m generators must be split if m is odd. If m is even, then the same is true if the degree of X is at least 3.

Let {f0, · · · , fn; g0, · · · , gn} be a sequence of homogeneous polynomials in 2n + 2 variables with no common zeroes in P and suppose that the degrees of the polynomials are such that Q = ∑n i=0 figi is a homogeneous polynomial. We shall refer to the hypersurface X defined by Q as a generalised quadric. In this note, we prove that generalised quadrics in… (More)

This paper draws out some implications of son targeting fertility behaviour for gender inequality. It is demonstrated that such behaviour has two notable implications at the aggregate level: (a)larger number of siblings for girls (Sibling Effect), and (b)a higher within-family birth order for boys (Birth Order Effect). While the first tends to worsen gender… (More)