arXiv subjects

Jaya N. N. Iyer

Publications and source records attributed to Jaya N. N. Iyer.

4 recordsLinked to original sources

arXiv2015

Cohomological invariants of a variation of flat connection

In this paper, we apply the theory of Chern-Cheeger-Simons to construct canonical invariants associated to a $r$-simplex whose points parametrize flat connections on a smooth manifold $X$. These invariants lie in degrees $(2p-r-1)$-cohomology with $C/Z$-coefficients, for $p> r\geq 1$. In turn, this corresponds to a homomorphism on the higher homology groups of the moduli space of flat connections, and taking values in $C/Z$-cohomology of the underlying smooth manifold $X$.

math.DG↗

arXiv2014

Stability of tangent bundle on the moduli space of stable bundles on a curve

In this paper, we prove that the tangent bundle of the moduli space $\cSU_C(r,d)$ of stable bundles of rank $r>2$ and of fixed determinant of degree $d$ (such that $(r,d)=1$), on a smooth projective curve $C$ is always stable, in the sense of Mumford-Takemoto. This verifies a well-known conjecture, and is related to a conjectural existence of a Kähler-Einstein metric on Fano varieties with Picard number one.

math.AG↗

arXiv2012

Semistability of logarithmic cotangent bundle on some projective manifolds

In this paper, we investigate the semistability of logarithmic de Rham sheaves on a smooth projective variety, under suitable conditions. In particular when the Picard number is one, we obtain results for any log Del Pezzo surface, log Fano threefolds, and for log Fano $n$-folds of dimension $n\leq 6$.

math.AG↗

arXiv2006

Chern invariants of some flat bundles in the arithmetic Deligne cohomology

In this note, we investigate the Chern classes of flat bundles in the arithmetic Deligne Cohomology, introduced by Green-Griffiths, Asakura-Saito. We show nontriviality of the Chern classes in some cases and the proof also indicates that generic flat bundles (in its moduli space) can be expected to have nontrivial classes, which is in contrast with some Gauss-Manin systems.

math.AG↗