Computations of generalized Dolbeault cohomology

It is shown that D=4N=1 SUSY Yang-Mills theory with an appropriate supermultiplet of matter can be twisted on a compact Kähler manifold. The conditions for cancellation of anomalies of BRST charge are found. The twisted theory has an appropriate BRST charge. We find a nontrivial set of physical operators defined as classes of the cohomology of this BRST operator. We prove that the physical correlators are independent of the external Kähler metric up to a power of a ratio of two Ray-Singer torsions for the Dolbeault cohomology complex on a Kähler manifold. The correlators of local physical operators turn out to be independent of antiholomorphic coordinates defined with a complex structure on the Kähler manifold. However, a dependence of the correlators on holomorphic coordinates can still remain. For a hyper-Kähler metric the physical correlators turn out to be independent of all coordinates of insertions of local physical operators.

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Intertwining ladder representations for SU(p, q) into Dolbeault cohomology

Noncommutative Harmonic Analysis - Progress in Mathematics ◽

10.1007/978-0-8176-8204-0_14 ◽

2004 ◽

pp. 395-418

Author(s):

John D. Lorch ◽

Lisa A. Mantini ◽

Jodie D. Novak

Keyword(s):

Dolbeault Cohomology ◽

Ladder Representations

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Locally residual currents and Dolbeault cohomology on projective manifolds

Bulletin des Sciences Mathématiques ◽

10.1016/j.bulsci.2006.04.002 ◽

2006 ◽

Vol 130 (6) ◽

pp. 553-564 ◽

Cited By ~ 2

Author(s):

Bruno Fabre

Keyword(s):

Dolbeault Cohomology ◽

Residual Currents ◽

Projective Manifolds

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Kirwan surjectivity for the equivariant Dolbeault cohomology

Journal of Geometry and Physics ◽

10.1016/j.geomphys.2019.05.005 ◽

2019 ◽

Vol 144 ◽

pp. 43-53

Author(s):

Yi Lin

Keyword(s):

Dolbeault Cohomology

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ON THE ANNIHILATOR OF A DOLBEAULT GROUP

International Journal of Mathematics ◽

10.1142/s0129167x10006045 ◽

2010 ◽

Vol 21 (03) ◽

pp. 317-331

Author(s):

IMRE PATYI

Keyword(s):

Holomorphic Function ◽

Open Subset ◽

Cohomology Group ◽

Holomorphic Functions ◽

Dolbeault Cohomology ◽

Infinite Dimensional ◽

Continuous Character

We show that any Dolbeault cohomology group Hp,q(D), p ≥ 0, q ≥ 1, of an open subset D of a closed finite codimensional complex Hilbert submanifold of ℓ2 is either zero or infinite dimensional. We also show that any continuous character of the algebra of holomorphic functions of a closed complex Hilbert submanifold M of ℓ2 is induced by its evaluation at a point of M. Lastly, we prove that any closed split infinite dimensional complex Banach submanifold of ℓ2 admits a nowhere critical holomorphic function.

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