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On localization in holomorphic equivariant cohomology

100%

Bruzzo U., Rubtsov V.

Open Mathematics

2012

tom 10

nr 4

1442-1454

We study a holomorphic equivariant cohomology built out of the Atiyah algebroid of an equivariant holomorphic vector bundle and prove a related localization formula. This encompasses various residue formulas in complex geometry, in particular we shall show that it contains as special cases Carrell-Liebermann’s and Feng-Ma’s residue formulas, and Baum-Bott’s formula for the zeroes of a meromorphic vector field.

Moduli of symplectic instanton vector bundles of higher rank on projective space ℙ3

81%

Bruzzo U., Markushevich D., Tikhomirov A.

Open Mathematics

2012

tom 10

nr 4

1232-1245

Symplectic instanton vector bundles on the projective space ℙ3 constitute a natural generalization of mathematical instantons of rank-2. We study the moduli space I n;r of rank-2r symplectic instanton vector bundles on ℙ3 with r ≥ 2 and second Chern class n ≥ r, n ≡ r (mod 2). We introduce the notion of tame symplectic instantons by excluding a kind of pathological monads and show that the locus I n;r* of tame symplectic instantons is irreducible and has the expected dimension, equal to 4n(r + 1) −r(2r + 1).

Ograniczanie wyników

2 Open Mathematics

2 Bruzzo U.

1 Markushevich D.

1 Rubtsov V.

1 Tikhomirov A.

2 2012

Wyniki wyszukiwania

On localization in holomorphic equivariant cohomology

Moduli of symplectic instanton vector bundles of higher rank on projective space ℙ3