Non-commutative periods and Mirror Symmetry in higher dimensions

Serguei Barannikov

Research output: Contribution to journalArticlepeer-review

10 Citations (Scopus)


We study an analog for higher-dimensional Calabi-Yau manifolds of the standard predictions of Mirror Symmetry. We introduce periods associated with "non-commutative" deformations of Calabi-Yau manifolds. These periods define a map M → ⊕kHk(Xn, ℂ) [n - k] on the moduli space of such deformations which is a local isomorphism. Using these non-commutative periods we introduce invariants of variations of semi-infinite generalized Hodge structures living over the moduli space M. It is shown that the generating function of such invariants satisfies the system of WDVV-equations exactly as in the case of Gromov-Witten invariants. We prove that the total collection of rational Gromov-Witten invariants of complete intersection Calabi-Yau manifold can be identified with the collection of invariants of variations of generalized (semi-infinite) Hodge structures attached to the mirror variety. The basic technical tool utilized is the deformation theory.

Original languageEnglish
Pages (from-to)281-325
Number of pages45
JournalCommunications in Mathematical Physics
Issue number2
Publication statusPublished - Jun 2002
Externally publishedYes


Dive into the research topics of 'Non-commutative periods and Mirror Symmetry in higher dimensions'. Together they form a unique fingerprint.

Cite this