4 citations · 11 across the 8 of their papers we have counts for
8 papers
Hypersymplectic manifolds and associated geometries
Varun Thakre
We investigate an obstruction for hypersymplectic manifolds equipped with a free, isometric action of SU(1,1). When the obstruction vanishes, we show that the manifold is a metric…
Generalised monopole equations on Kahler surfaces
Indranil Biswas, Varun Thakre
In this article, we establish a Hitchin-Kobayashi type correspondence for generalised Seiberg-Witten monopole equations on Kahler surfaces. We show that the "stability" criterion w…
Symplectic vortex equations for Kahler cones over Sasakian manifolds
Varun Thakre
We obtain a Hitchin-Kobayashi-type correspondence for symplectic vortex equations, with the target a Kahler cone over a compact Sasakian manifold. We show that the correspondence r…
Generalised Seiberg-Witten equations and almost-Hermitian geometry
Varun Thakre
In this article, we study a generalisation of the Seiberg-Witten equations, replacing the spinor representation with a hyperKahler manifold equipped with certain symmetries. Centra…
Kahler and symplectic structures on 4-manifolds and hyperKahler geometry
Varun Thakre
A non-linear generalization of the Dirac operator in 4-dimensions, obtained by replacing the spinor representation with a hyperKahler manifold admitting certain symmetries, is cons…
Genus two enumerative invariants in del-Pezzo surfaces with a fixed complex structure
Indranil Biswas, Ritwik Mukherjee, Varun Thakre
We obtain a formula for the number of genus two curves with a fixed complex structure of a given degree on a del-Pezzo surface that pass through an appropriate number of generic po…
Genus one enumerative invariants in del-Pezzo surfaces with a fixed complex structure
Indranil Biswas, Ritwik Mukherjee, Varun Thakre
We obtain a formula for the number of genus one curves with a fixed complex structure of a given degree on a del-Pezzo surface that pass through an appropriate number of generic po…
Generalized Seiberg-Witten equations on Riemann surface
Rukmini Dey, Varun Thakre
In this paper we consider twice-dimensionally reduced, generalized Seiberg-Witten equations, defined on a compact Riemann surface. A novel feature of the reduction technique is tha…