On Clifford double mirrors of toric complete intersections

Abstract

We present a construction of noncommutative double mirrors to complete intersections in toric varieties. This construction unifies existing sporadic examples and explains the underlying combinatorial and physical reasons for their existence.2. Review of reflexive Gorenstein cones, Batyrev-Borisov mirror construction and double mirror phenomenon.

On stringy Euler characteristics of Clifford non-commutative varieties

“…It is natural to try to extend our calculations to the case of Clifford double mirrors of complete intersections in toric varieties, described in [11]. Specifically, under some centrality and flatness assumptions, Theorem 6.3 of [11] shows that a complete intersection X and a Clifford non-commutative variety Y given by different decompositions of the degree element deg ∨ of a reflexive Gorenstein cone K ∨ and the appropriate regular simplicial fans in K ∨ have equivalent bounded derived categories. It is natural to conjecture that the Clifford-stringy Euler characteristics of Y and the Euler characteristics of complete intersections X in toric varieties are equal.…”

Movable vs Monodromy Nilpotent Cones of Calabi-Yau Manifolds

“…We can describe our birational Calabi-Yau threefolds in this general setting. See references [7,12] for recent works which shed light on this general phenomenon from the derived categories of Calabi-Yau threefolds.…”

Derived Partners of Enriques Surfaces

“…Borisov and Li proposed a toric framework to generalize the above construction. In particular, they argued the existence of a derived partner of Enriques surfaces (see [3,Section 9.2]), making use of the fact that all complex Enriques surfaces can be obtained as a quotient of (2, 2, 2)-complete intersection in P 5 by a fixed-point-free involution [7].…”