Arijit Dey

Bio: Arijit Dey is an academic researcher from Tata Institute of Fundamental Research. The author has contributed to research in topics: Vector bundle & Line bundle. The author has co-authored 3 publications. Previous affiliations of Arijit Dey include Max Planck Society.

Chen–Ruan cohomology of some moduli spaces of parabolic vector bundles

Abstract: Let ( X , D ) be an l-pointed compact Riemann surface of genus at least two. For each point x ∈ D , fix parabolic weights ( α 1 ( x ) , α 2 ( x ) ) such that ∑ x ∈ D ( α 1 ( x ) − α 2 ( x ) ) 1 / 2 . Fix a holomorphic line bundle ξ over X of degree one. Let P M ξ denote the moduli space of stable parabolic vector bundles, of rank two and determinant ξ, with parabolic structure over D and parabolic weights { ( α 1 ( x ) , α 2 ( x ) ) } x ∈ D . The group of order two line bundles over X acts on P M ξ by the rule E ∗ ⊗ L ↦ E ∗ ⊗ L . We compute the Chen–Ruan cohomology ring of the corresponding orbifold.

Bogomolov restriction theorem for Higgs bundles

Abstract: Let ( E , θ ) be a stable Higgs bundle of rank r on a smooth complex projective surface X equipped with a polarization H. Let C ⊂ X be a smooth complete curve with [ C ] = n ⋅ H . If 2 n > R r ( 2 r c 2 ( E ) − ( r − 1 ) c 1 ( E ) 2 ) , where R = max { ( r s ) ( r − 1 s − 1 ) : 1 ⩽ s ⩽ r − 1 } , then we prove that the restriction of ( E , θ ) to C is a stable Higgs bundle. This is a Higgs bundle analog of Bogomolov's restriction theorem for stable vector bundles.

Restriction of Tangent Bundle and Semistability

Abstract: Let G be a simple linear algebraic group defined over ℂ and P ⊂ G a maximal proper parabolic subgroup such that m: = dim ℂ G/P ≥ 5. Let ι: Z 1 ∩ Z 2↪G/P be a smooth complete intersection such that degree(Z i ) ≥ (m − 1)·index(G/P)/m, i = 1, 2. Then the vector bundle ι*T(G/P) → Z 1 ∩ Z 2 is semistable.

Chen–Ruan cohomology and moduli spaces of parabolic bundles over a Riemann surface

Abstract: Let $$(X,\,D)$$ be an m-pointed compact Riemann surface of genus at least 2. For each $$x \,\in \, D$$ , fix full flag and concentrated weight system $$\alpha $$ . Let $$P \mathcal {M}_{\xi }$$ denote the moduli space of semi-stable parabolic vector bundles of rank r and determinant $$\xi $$ over X with weight system $$\alpha $$ , where r is a prime number and $$\xi $$ is a holomorphic line bundle over X of degree d which is not a multiple of r. We compute the Chen–Ruan cohomology of the orbifold for the action on $$P \mathcal {M}_{\xi }$$ of the group of r-torsion points in $$\mathrm{Pic}^0(X)$$ .

Chen--Ruan cohomology and orbifold Euler characteristic of moduli spaces of parabolic bundles

Abstract: A BSTRACT . We consider the moduli space of stable parabolic Higgs bundles of rank 𝑟 and fixed determinant, and having full flag quasi-parabolic structures over an arbitrary parabolic divisor on a smooth complex projective curve 𝑋 of genus 𝑔 , with 𝑔 ≥ 2 . The group Γ of 𝑟 -torsion points of the Jacobian of 𝑋 acts on this moduli space. We describe the connected components of the various fixed point loci of this moduli under non-trivial elements from Γ . When the Higgs field is zero, or in other words when we restrict ourselves to the moduli of stable parabolic bundles, we also compute the orbifold Euler characteristic of the corresponding global quotient orbifold. We also describe the Chen–Ruan cohomology groups of this orbifold under certain conditions on the rank and degree, and describe the Chen–Ruan product structure in special cases.