Orbifold quantum Riemann–Roch, Lefschetz and Serre

By Hsian-Hua Tseng. 2005

149 citations recorded by the source corpus.

Given a vector bundle $F$ on a smooth Deligne-Mumford stack $\X$ and an invertible multiplicative characteristic class $\bc$, we define the orbifold Gromov-Witten invariants of $\X$ twisted by $F$ and $\bc$. We prove a "quantum Riemann-Roch theorem" which expresses the generating function of the twisted invariants in terms of the generating function of the untwisted invariants. A Quantum Lefschetz Hyperplane Theorem is derived from this by specializing to genus zero. As an application, we determine the relationship between genus-0 orbifold Gromov-Witten invariants of $\X$ and that of a complete intersection. This provides a way to verify mirror symmetry predictions for complete intersection orbifolds.

Subfields: Discrete Mathematics and Combinatorics, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/f2389d5f0f154f5838619a54fd63d1ba3a25d7f3

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Citations in the corpus

Quantum Cohomology and Periods (2011, methodology): “Applying Tseng’s symplectic operator ∆tw ([55]; we use the convention in [16, Theorem 4.”
LOCALIZATION IN GROMOV-WITTEN THEORY AND ORBIFOLD GROMOV-WITTEN THEORY (2011, methodology): “By Tseng’s orbifold quantum Riemann-Roch theorem [57], Hurwitz-Hodge integrals can be reconstructed from descendant integrals on Mg,~c(BG):”
An integral structure in quantum cohomology and mirror symmetry for toric orbifolds (2009, unknown): “where Qd is the element of the group ring C[EﬀX] corresponding to d∈ EﬀX. We decompose τ∈ H∗ orb(X) as (3) τ= τ0,2 +τ ′, τ 0,2 ∈ H 2(X), τ′ ∈ M k6=1 H2k(X) ⊕ M v∈T′ H∗(Xv). Using the divisor equation [69, 2], we ﬁnd α•τ β= X d∈EﬀX X l≥0 XN k=1 1 l! α,β,τ′,...,τ′,φ k X 0,l+3,d (4) ehτ0,2,diQdφk. Ther”
The Crepant Transformation Conjecture for Toric Complete Intersections (2014, background): “ntal solutions for the quantum connections on the ambient parts H amb (Y ). The proof of Theorem1.4relies on the Mirror Theorem for toric complete intersections [31], and on non-linear Serre duality [32,42,43,74], which relates the quantum cohomology of Y to the quantum cohomology of the total space”
The Hirzebruch--Riemann--Roch theorem in true genus-0 quantum K-theory (2011, methodology): “putation by Jarvis–Kimura of such invariants in the case when the target is the quotient of a point (or more generally a manifold) by the trivial action of a ﬁnite group. Next is the theorem of Tseng [24] expressing twisted GW-invariants of orbifold target spaces in terms of untwisted ones. Yet, two”
Orbifold quasimap theory (2014, methodology): “ considerations from Remark 3.15 with Theorem 4.3 and the calculations of this section provides a diﬀerent ORBIFOLD QUASIMAP THEORY 41 proof (not relying on Tseng’s orbifold Quantum Lefschetz theorem [31]) of the Mirror Theorem for complete intersections of convex hypersurfaces in toric DM stacks of”