Abstract
We leverage the results of the prequel [8], in combination with a theorem of D. Orlov to create a categorical covering picture for factorizations. As applications, we provide a conjectural geometric framework to further understand M. Kontsevich's Homological Mirror Symmetry conjecture and obtain new cases of a conjecture of Orlov concerning the Rouquier dimension of the bounded derived category of coherent sheaves on a smooth variety.
| Original language | English (US) |
|---|---|
| Pages (from-to) | 702-757 |
| Number of pages | 56 |
| Journal | Journal des Mathematiques Pures et Appliquees |
| Volume | 102 |
| Issue number | 4 |
| DOIs | |
| State | Published - Oct 1 2014 |
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Keywords
- Derived categories
- Homological Mirror Symmetry
- Matrix factorizations
- Rouquier dimension
ASJC Scopus subject areas
- Applied Mathematics
- Mathematics(all)
Cite this
A category of kernels for equivariant factorizations, II : Further implications. / Ballard, Matthew; Favero, David; Katzarkov, Ludmil.
In: Journal des Mathematiques Pures et Appliquees, Vol. 102, No. 4, 01.10.2014, p. 702-757.Research output: Contribution to journal › Article
}
TY - JOUR
T1 - A category of kernels for equivariant factorizations, II
T2 - Further implications
AU - Ballard, Matthew
AU - Favero, David
AU - Katzarkov, Ludmil
PY - 2014/10/1
Y1 - 2014/10/1
N2 - We leverage the results of the prequel [8], in combination with a theorem of D. Orlov to create a categorical covering picture for factorizations. As applications, we provide a conjectural geometric framework to further understand M. Kontsevich's Homological Mirror Symmetry conjecture and obtain new cases of a conjecture of Orlov concerning the Rouquier dimension of the bounded derived category of coherent sheaves on a smooth variety.
AB - We leverage the results of the prequel [8], in combination with a theorem of D. Orlov to create a categorical covering picture for factorizations. As applications, we provide a conjectural geometric framework to further understand M. Kontsevich's Homological Mirror Symmetry conjecture and obtain new cases of a conjecture of Orlov concerning the Rouquier dimension of the bounded derived category of coherent sheaves on a smooth variety.
KW - Derived categories
KW - Homological Mirror Symmetry
KW - Matrix factorizations
KW - Rouquier dimension
UR - http://www.scopus.com/inward/record.url?scp=84908042765&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=84908042765&partnerID=8YFLogxK
U2 - 10.1016/j.matpur.2014.02.004
DO - 10.1016/j.matpur.2014.02.004
M3 - Article
AN - SCOPUS:84908042765
VL - 102
SP - 702
EP - 757
JO - Journal des Mathematiques Pures et Appliquees
JF - Journal des Mathematiques Pures et Appliquees
SN - 0021-7824
IS - 4
ER -