On stringy Euler characteristics of Clifford non-commutative varieties

Lev Borisov, Chengxi Wang

Research output: Contribution to journalArticlepeer-review

1 Scopus citations


It was shown by Kuznetsov that complete intersections of n generic quadrics in P 2n−1 are related by Homological Projective Duality to certain non-commutative (Clifford) varieties which are in some sense birational to double covers of P n−1 ramified over symmetric determinantal hypersurfaces. Mirror symmetry predicts that the Hodge numbers of the complete intersections of quadrics must coincide with the appropriately defined Hodge numbers of these double covers. We observe that these numbers must be different from the well-known Batyrev's stringy Hodge numbers, else the equality fails already at the level of Euler characteristics. We define a natural modification of stringy Hodge numbers for the particular class of Clifford varieties, and prove the corresponding equality of Euler characteristics in arbitrary dimension.

Original languageAmerican English
Pages (from-to)1117-1150
Number of pages34
JournalAdvances in Mathematics
StatePublished - Jun 20 2019

ASJC Scopus subject areas

  • Mathematics(all)


  • Clifford algebras
  • Euler characteristics
  • Quadric fibrations


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