On stringy Euler characteristics of Clifford non-commutative varieties

TY - JOUR

T1 - On stringy Euler characteristics of Clifford non-commutative varieties

AU - Borisov, Lev

AU - Wang, Chengxi

N1 - Funding Information: Acknowledgments. L.B. has been partially supported by National Science Foundation grant DMS-1601907. We thank the anonymous referee for multiple useful suggestions. Publisher Copyright: © 2019

PY - 2019/6/20

Y1 - 2019/6/20

N2 - 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.

AB - 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.

KW - Clifford algebras

KW - Euler characteristics

KW - Quadric fibrations

UR - http://www.scopus.com/inward/record.url?scp=85064953122&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85064953122&partnerID=8YFLogxK

U2 - https://doi.org/10.1016/j.aim.2019.04.040

DO - https://doi.org/10.1016/j.aim.2019.04.040

M3 - Article

SN - 0001-8708

VL - 349

SP - 1117

EP - 1150

JO - Advances in Mathematics

JF - Advances in Mathematics

ER -