Vellore Institute of Technology (VIT) is a private university located in&nbsp;Tamil Nadu, India. Founded in 1984, as Vellore Engineering College, the institution offers 20 undergraduate, 34 postgraduate, four integrated and four research programs. It has campuses in Vellore, Amravati, Bhopal and Chennai.

VIT is one of the top ranked private universities in India according to NIRF, THE and QS Rankings.&nbsp;Govt. of India has recognized&nbsp;VIT, Vellore as an&nbsp;Institution of Eminence. This has allowed VIT to take independent quality initiatives and move up in world ranking.

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VIT University

Let {\$}\backslashSym{\^{}}m X{\$} denote the {\$}m{\$}-th symmetric power of a smooth projective curve {\$}X{\$}. Let {\$}\backslashwt{\{}\backslashSym{\^{}}m X{\}}{\$} be the blow up of {\$}\backslashSym{\^{}}m X{\$} along some non-singular subvariety. In this note we are going to discuss when the pushforward homomorphism induced by the natural morphism from {\$}\backslashwt{\{}\backslashSym{\^{}}m X{\}}{\$} to {\$}\backslashSym{\^{}}n X{\$} is injective at the level of Chow groups for {\$}m\backslashleq n{\$}. Also we are going to prove that base changes of embeddings of one symmetric power into another, with respect to closed embeddings induces an injection at the level of Chow groups.

Department of Mathematics

School of Advanced Sciences

Vellore Campus

arXiv preprint arXiv:1609.

Blow ups and base changes of symmetric powers and Chow groups

In this text we prove that if a smooth cubic in $\PR^5$ has its Fano variety of lines birational to the Hilbert scheme of two points on a K3 surface, then there exists a smooth projective curve or a smooth projective surface embedded in the Fano variety, such that the kernel of the push-forward (at the level of zero cycles ) induced by the closed embedding is torsion.

Algebraic cycles on the Fano variety of lines of a cubic fourfold

In this note we are going to consider a smooth projective surface equipped with an involution and study the action of the involution at the level of Chow group of zero cycles.

arXiv preprint arXiv:1610.

Involutions on algebraic surfaces and zero cycles

In this note we prove that the kernel of the push-forward homomorphism on $d$-cycles modulo rational equivalence, induced by the closed embedding of an ample divisor linearly equivalent to some multiple of the theta divisor inside the Jacobian variety $J(C)$ is trivial. Here $C$ is a smooth projective curve of genus $g$.

World University root node

arXiv preprint arXiv:1504.

On the kernel of the push-forward homomorphism between Chow groups

Let {$}k{$} be an uncountable algebraically closed field of characteristic zero and let {$}\backslashmathscr X{$} be a nonsingular cubic hypersurface in {$}\backslashmathbb P{\^{}}5{$} over {$}k{$}. We prove that, for a very general hyperplane section {$}\backslashmathscr Y{$} of the cubic {$}\backslashmathscr X{$}, there exists a countable set {$}\backslashXi {$} of closed points on the Prymian of {$}\backslashmathscr Y{$}, such that, if {$}\backslashSigma {$} and {$}\backslashSigma '{$} are two linear combinations of lines of the same degree on {$}\backslashmathscr Y{$}, then {$}\backslashSigma {$} is rationally equivalent to {$}\backslashSigma '{$} on {$}\backslashmathscr X{$} if and only if the cycle class of {$}\backslashSigma -\backslashSigma '{$}, as a point on the Prymian, is an element of {$}\backslashXi {$}.

arXiv preprint arXiv:1405.

Rational equivalence for line configurations on cubic hypersurfaces in P^5

In the thesis we study codimension p algebraic cycles on a 2p-dimensional nonsingular projective variety X de�ned over an uncountable algebraically closed ground �eld k of characteristic 0. The main result (Theorem 4.7.1 in the thesis) says that, under some weak representability assumptions on the continuous parts of the Chow groups of the variety X and its nonsingular hyperplane sections Y , the kernel of the Gysin homomorphism from the codimension p Chow group of the very general Y to the codimension p + 1 Chow group of X is countable. As an application, we obtain the following concrete result. Let X be a nonsingular cubic hypersurface in P5 over k. Then, for a very general Y , there exists a countable set � of closed points on the Prym variety of the threefold Y , such that, if � and �0 are two linear combinations of lines of the same degree on Y , the one-cycle � is rationally equivalent to the one-cycle �0 on X if and only if the di�erence �