A Geometric Approach to Orlov's Theorem

Mathematics – Algebraic Geometry

Scientific paper

Rate now

  [ 0.00 ] – not rated yet Voters 0   Comments 0

Details

27 pages. Extensively revised from previous version. Final version to appear in Compositio Mathematica

Scientific paper

A 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 be a projective hypersurface. Already, Segal has established an equivalence between Orlov's category of graded matrix factorizations and the category of graded D-branes on the canonical bundle K of the ambient projective space. To complete the picture, I give an equivalence between the homotopy category of graded D-branes on K and Dcoh(X). This can be achieved directly and by deforming K to the normal bundle of X, embedded in K and invoking a global version of Kn\"{o}rrer periodicity. We also discuss an equivalence between graded D-branes on a general smooth quasi-projective variety and on the formal neighborhood of the singular locus of the zero fiber of the potential.

No associations

LandOfFree

Say what you really think

Search LandOfFree.com for scientists and scientific papers. Rate them and share your experience with other people.

Rating

A Geometric Approach to Orlov's Theorem 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 A Geometric Approach to Orlov's Theorem, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and A Geometric Approach to Orlov's Theorem will most certainly appreciate the feedback.

Rate now

     

Profile ID: LFWR-SCP-O-297232

  Search
All data on this website is collected from public sources. Our data reflects the most accurate information available at the time of publication.