arXiv subjects

V. Shende

Publications and source records attributed to V. Shende.

2 recordsLinked to original sources

arXiv2014

A short proof of the Göttsche conjecture

We prove that for a sufficiently ample line bundle $L$ on a surface $S$, the number of $δ$-nodal curves in a general $δ$-dimensional linear system is given by a universal polynomial of degree $δ$ in the four numbers $L^2,\,L.K_S,\,K_S^2$ and $c_2(S)$. The technique is a study of Hilbert schemes of points on curves on a surface, using the BPS calculus of [PT3] and the computation of tautological integrals on Hilbert schemes by Ellingsrud, Göttsche and Lehn. We are also able to weaken the ampleness required, from Göttsche's $(5δ-1)$-very ample to $δ$-very ample.

math.AG↗

arXiv2011

Large N duality, lagrangian cycles, and algebraic knots

We consider knot invariants in the context of large $N$ transitions of topological strings. In particular we consider aspects of Lagrangian cycles associated to knots in the conifold geometry. We show how these can be explicity constructed in the case of algebraic knots. We use this explicit construction to explain a recent conjecture relating study of stable pairs on algebraic curves with HOMFLY polynomials. Furthermore, for torus knots, using the explicit construction of the Lagrangian cycle, we also give a direct A-model computation and recover the HOMFLY polynomial for this case.

hep-th↗