Gepner type stability conditions on graded matrix factorizations

We introduce the notion of Gepner type Bridgeland stability conditions on triangulated categories, which depends on a choice of an autoequivalence and a complex number. We conjecture the existence of Gepner type stability conditions on the triangulated categories of graded matrix factorizations of weighted homogeneous polynomials. Such a stability condition may give a natural stability condition for Landau-Ginzburg B-branes, and correspond to the Gepner point of the stringy Kahler moduli space of a quintic 3-fold. The main result is to show our conjecture when the variety defined by the weighted homogeneous polynomial is a complete intersection of hyperplanes in a Calabi-Yau manifold with dimension less than or equal to two.

[1]  Yukinobu Toda.  Gepner point and strong Bogomolov-Gieseker inequality for quintic 3-folds , 2013, 1305.0345.

[2]  K. Ueda.  Hyperplane sections and stable derived categories , 2012, 1207.1167.

[3]  Yukinobu Toda.  Stability conditions and curve counting invariants on Calabi–Yau 3-folds , 2011, 1103.4229.

[4]  Matthew R. Ballard,et al.  Orlov spectra: bounds and gaps , 2010, 1012.0864.

[5]  A. Polishchuk,et al.  Matrix factorizations and Cohomological Field Theories , 2011, 1105.2903.

[6]  Arend Bayer,et al.  Bridgeland stability conditions on threefolds I: Bogomolov-Gieseker type inequalities , 2011, 1103.5010.

[7]  Arend Bayer,et al.  The space of stability conditions on the local projective plane , 2009, 0912.0043.

[8]  G. Moore,et al.  Split states, entropy enigmas, holes and halos , 2007, hep-th/0702146.

[9]  T. Bridgeland.  Hall algebras and curve-counting invariants , 2010, 1002.4374.

[10]  A. Polishchuk,et al.  Chern characters and Hirzebruch-Riemann-Roch formula for matrix factorizations , 2010, 1002.2116.

[11]  Tobias Dyckerhoff.  Compact generators in categories of matrix factorizations , 2009, 0904.4713.

[12]  Yukinobu Toda.  Curve counting theories via stable objects I. DT/PT correspondence , 2009, 0902.4371.

[13]  A. Polishchuk,et al.  Gluing Stability Conditions , 2009, 0902.0323.

[14]  Y. Ruan,et al.  Landau–Ginzburg/Calabi–Yau correspondence for quintic three-folds via symplectic transformations , 2008, 0812.4660.

[15]  Yan Soibelman,et al.  Stability structures, motivic Donaldson-Thomas invariants and cluster transformations , 2008, 0811.2435.

[16]  Yinan Song,et al.  A theory of generalized Donaldson–Thomas invariants , 2008, 0810.5645.

[17]  Yukinobu Toda.  Generating functions of stable pair invariants via wall-crossings in derived categories , 2008, 0806.0062.

[18]  Yukinobu Toda.  Limit stable objects on Calabi-Yau 3-folds , 2008, 0803.2356.

[19]  Tyler Jarvis,et al.  The Witten equation and its virtual fundamental cycle , 2007, 0712.4025.

[20]  P. Newstead,et al.  Clifford’s theorem for coherent systems , 2007, 0707.4046.

[21]  Yukinobu Toda.  Moduli stacks and invariants of semistable objects on K3 surfaces , 2007, math/0703590.

[22]  A. Takahashi,et al.  Matrix factorizations and representations of quivers II: Type ADE case , 2005, math/0511155.

[23]  A. Takahashi.  Matrix Factorizations and Representations of Quivers I , 2005, math/0506347.

[24]  D. Orlov,et al.  Derived Categories of Coherent Sheaves and Triangulated Categories of Singularities , 2005, math/0503632.

[25]  J. Walcher.  Stability of Landau-Ginzburg branes , 2004, hep-th/0412274.

[26]  H. Ooguri,et al.  Black hole attractors and the topological string , 2004, hep-th/0405146.

[27]  A. Căldăraru.  The Mukai pairing, II: the Hochschild-Kostant-Rosenberg isomorphism , 2003, math/0308080.

[28]  T. Bridgeland.  Stability conditions on $K3$ surfaces , 2003, math/0307164.

[29]  T. Bridgeland.  Stability conditions on triangulated categories , 2002, math/0212237.

[30]  Richard P. Thomas,et al.  Braid group actions on derived categories of coherent sheaves , 2000, math/0001043.

[31]  I. Reiten,et al.  Tilting in Abelian Categories and Quasitilted Algebras , 1996 .

[32]  H. Knörrer.  Cohen-Macaulay modules on hypersurface singularities I , 1987 .

[33]  Kyoji Saito.  Regular System of Weights and Associated Singularities , 1987 .