arXiv subjects

Kapil H. Paranjape

Publications and source records attributed to Kapil H. Paranjape.

3 recordsLinked to original sources

arXiv2000

Higher Abel-Jacobi Maps

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.

math.AG↗

arXiv2000

The Hodge Conjecture for general Prym varieties

The space of Hodge cycles of the general Prym variety is proved to be generated by its Neron-Severi group.

math.AG↗

arXiv1992

Cohomological and Cycle-theoretic connectivity

One of the themes in algebraic geometry is the study of the relation between the ``topology'' of a smooth projective variety and a (``general'') hyperplane section. Recent results of Nori produce cohomological evidence for a conjecture that a general hypersurface of sufficently large degree should have no ``interesting'' cycles. We compute precise bounds for these results and show by example that there are indeed interesting cycles for degrees that are not high enough. In a different direction Esnault, Nori and Srinivas have shown connectivity for intersections of small multidegree. We show analogous cycle-theoretic connectivity results.

alg-geom↗