2010

The Kapustin-Li formula revisited

Dyckerhoff, Tobias, Murfet, Daniel

Understand

We provide a new perspective on the Kapustin-Li formula for the duality pairing on the morphism complexes in the matrix factorization category of an isolated hypersurface singularity.

In our context, the formula arises as an explicit description of a local duality isomorphism, obtained by using the basic perturbation lemma and Grothendieck residues.
The non-degeneracy of the pairing becomes apparent in this setting.
Further, we show that the pairing lifts to a Calabi-Yau structure on the matrix factorization category.

Built on

Hirzebruch-Riemann-Roch theorem for DG algebras, 2007, arXiv:0710.1937
Original
D. Shklyarov · 1937
Earlier work this paper cites.
Residues and duality
R. Hartshorne · 1966
Earlier work this paper cites.
Local cohomology
R. Hartshorne · 1967
Earlier work this paper cites.
Functors and morphisms determined by objects
M. Auslander · 1978
Earlier work this paper cites.
Principles of algebraic geometry
P. Griffiths and J. Harris · 1978
Earlier work this paper cites.
Homological algebra on a complete intersection, with an application to group representations
D. Eisenbud · 1980
Earlier work this paper cites.
Dualizing sheaves, differentials and residues on algebraic varieties
J. Lipman · 1984
Earlier work this paper cites.
Isolated singular points on complete intersections
E. J. N. Looijenga · 1984
Earlier work this paper cites.
Maximal Cohen-Macaulay modules and Tate-Cohomology over Gorenstein rings
R.-O. Buchweitz · 1986
Earlier work this paper cites.

Similar

Kähler differentials
Ernst Kunz · 1986
Cited alongside, same era.
Cohen—Macaulay modules over Cohen—Macaulay Rings
Y. Yoshino · 1990
Cited alongside, same era.
Cohen-Macaulay rings
W. Bruns and J. Herzog · 1993
Cited alongside, same era.
On the perturbation lemma, and deformations
M. Crainic · 2004
Cited alongside, same era.
On the relation between open and closed topological strings
A. Kapustin and L. Rozansky · 2004
Cited alongside, same era.
Notes on A-infinity algebras, A-infinity categories and non-commutative geometry. I, 2006, arXiv:math/0606241
M. Kontsevich and Y. Soibelman · 2006
Cited alongside, same era.
Lectures on DG-categories, 2006
B. Toën · 2006
Cited alongside, same era.
Topological conformal field theories and Calabi-Yau categories
K. Costello · 2007
Cited alongside, same era.
The homotopy theory of d g dg -categories and derived Morita theory
B. Toën · 2007
Cited alongside, same era.

Then

Residues and duality for projective algebraic varieties
E. Kunz · 2008
Later among the works it cites.
Matrix factorisations and open topological string theory
N. Carqueville · 2009
Later among the works it cites.
Compact generators in categories of matrix factorizations, 2009, arXiv:math/0904.4713
T. Dyckerhoff · 2009
Later among the works it cites.
On the Classification of Topological Field Theories, 2009, arXiv:math/0905.0465
J. Lurie · 2009
Later among the works it cites.
Residues and duality for singularity categories of isolated Gorenstein singularities, 2009, arXiv:math/0912.1629
D. Murfet · 2009
Later among the works it cites.
The closed state space of affine Landau-Ginzburg B-models, 2009, arXiv:math/0904.1339
E. Segal · 2009
Later among the works it cites.
Notes on Kontsevich-Soibelman’s theorem about cyclic A-infinity algebras, 2010, arXiv:1002.3653v2
Original
C.-H. Cho and S. Lee · 2010
Closest in time.
Chern characters and Hirzebruch-Riemann-Roch formula for matrix factorizations, 2010, arXiv:math/1002.2116
A. Polishchuk and A. Vaintrob · 2010
Closest in time.

Beyond the bibliography

alphaXiv searches the wider corpus for related work and actual follow-ups.

Open on alphaXiv

alphaXiv is searching for related work…

Reading the bibliography…