Mathematics – Algebraic Geometry
Scientific paper
2011-01-30
Mathematics
Algebraic Geometry
78 pages. Draft
Scientific paper
The derived category of a hypersurface has an action by "cohomology operations" k[t], deg t=-2, underlying the 2-periodic structure on its category of singularities (as matrix factorizations). We prove a Thom-Sebastiani type Theorem, identifying the k[t]-linear tensor products of these dg categories with coherent complexes on the zero locus of the sum potential on the product (with a support condition), and identify the dg category of colimit-preserving k[t]-linear functors between Ind-completions with Ind-coherent complexes on the zero locus of the difference potential (with a support condition). These results imply the analogous statements for the 2-periodic dg categories of matrix factorizations. Some applications include: we refine and establish the expected computation of 2-periodic Hochschild invariants of matrix factorizations; we show that the category of matrix factorizations is smooth, and is proper when the critical locus is proper; we show how Calabi-Yau structures on matrix factorizations arise from volume forms on the total space; we establish a version of Kn\"orrer Periodicity for eliminating metabolic quadratic bundles over a base.
No associations
LandOfFree
Thom-Sebastiani & Duality for Matrix Factorizations does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Thom-Sebastiani & Duality for Matrix Factorizations, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Thom-Sebastiani & Duality for Matrix Factorizations will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-646778