scholarly journals The triangular spectrum of matrix factorizations is the singular locus

2016 ◽  
Vol 144 (8) ◽  
pp. 3283-3290 ◽  
Author(s):  
Xuan Yu
Keyword(s):  
Singular Locus ◽  
Matrix Factorizations

scholarly journals A geometric approach to Orlov’s theorem

2012 ◽  
Vol 148 (5) ◽  
pp. 1365-1389 ◽  
Author(s):  
Ian Shipman
Keyword(s):  
Normal Bundle ◽  
Geometric Approach ◽  
Singular Locus ◽  
Matrix Factorizations ◽  
Canonical Bundle ◽  
Algebraic Construction ◽  
Famous Theorem ◽  
Projective Hypersurface ◽  
Coherent Sheaves ◽  
Formal Neighborhood

AbstractA famous theorem of D. Orlov describes the derived bounded category of coherent sheaves on projective hypersurfaces in terms of an algebraic construction called graded matrix factorizations. In this article, I implement a proposal of E. Segal to prove Orlov’s theorem in the Calabi–Yau setting using a globalization of the category of graded matrix factorizations (graded D-branes). Let X⊂ℙ be a projective hypersurface. Segal has already established an equivalence between Orlov’s category of graded matrix factorizations and the category of graded D-branes on the canonical bundle Kℙ to ℙ. To complete the picture, I give an equivalence between the homotopy category of graded D-branes on Kℙ and Dbcoh(X). This can be achieved directly, as well as by deforming Kℙ to the normal bundle of X⊂Kℙ and invoking a global version of Knörrer periodicity. We also discuss an equivalence between graded D-branes on a general smooth quasiprojective variety and on the formal neighborhood of the singular locus of the zero fiber of the potential.

scholarly journals Relative singular locus and Balmer spectrum of matrix factorizations

2018 ◽  
Vol 371 (7) ◽  
pp. 4993-5021
Author(s):  
Yuki Hirano
Keyword(s):  
Singular Locus ◽  
Matrix Factorizations

scholarly journals Towards the classification of rank-r $$ \mathcal{N} $$ = 2 SCFTs. Part I. Twisted partition function and central charge formulae

2020 ◽  
Vol 2020 (12) ◽  
Author(s):  
Mario Martone
Keyword(s):  
Partition Function ◽  
Central Charge ◽  
Singular Locus ◽  
Companion Paper ◽  
Coulomb Branch ◽  
Energy Limit ◽  
Superconformal Field Theories ◽  
Rank 2 ◽  
Explicit Formulae

Abstract We derive explicit formulae to compute the a and c central charges of four dimensional $$ \mathcal{N} $$ N = 2 superconformal field theories (SCFTs) directly from Coulomb branch related quantities. The formulae apply at arbitrary rank. We also discover general properties of the low-energy limit behavior of the flavor symmetry of $$ \mathcal{N} $$ N = 2 SCFTs which culminate with our $$ \mathcal{N} $$ N = 2 UV-IR simple flavor condition. This is done by determining precisely the relation between the integrand of the partition function of the topologically twisted version of the 4d $$ \mathcal{N} $$ N = 2 SCFTs and the singular locus of their Coulomb branches. The techniques developed here are extensively applied to many rank-2 SCFTs, including new ones, in a companion paper.This manuscript is dedicated to the memory of Rayshard Brooks, George Floyd, Breonna Taylor and the countless black lives taken by US police forces and still awaiting justice. Our hearts are with our colleagues of color who suffer daily the consequences of this racist world.

scholarly journals Noncommutative Matrix Factorizations with an Application to Skew Exterior Algebras

2021 ◽  
Author(s):  
Izuru Mori ◽  
Kenta Ueyama
Keyword(s):  
Matrix Factorizations

scholarly journals Algorithm-based fault tolerance for dense matrix factorizations

2012 ◽  
Author(s):  
Peng Du ◽  
Aurelien Bouteiller ◽  
George Bosilca ◽  
Thomas Herault ◽  
Jack Dongarra
Keyword(s):  
Fault Tolerance ◽  
Matrix Factorizations ◽  
Dense Matrix

scholarly journals Rigorous Perturbation Bounds of Some Matrix Factorizations

2010 ◽  
Vol 31 (5) ◽  
pp. 2841-2859 ◽  
Author(s):  
X.-W. Chang ◽  
D. Stehlé
Keyword(s):  
Matrix Factorizations ◽  
Perturbation Bounds

Integrity and normality. The singular locus

1988 ◽  
pp. 64-72
Author(s):  
Winfried Bruns ◽  
Udo Vetter
Keyword(s):  
Singular Locus

scholarly journals Matrix factorizations and link homology II

2008 ◽  
Vol 12 (3) ◽  
pp. 1387-1425 ◽  
Author(s):  
Mikhail Khovanov ◽  
Lev Rozansky
Keyword(s):  
Matrix Factorizations ◽  
Link Homology
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