旗簇等变定向上同调的Leray-Hirsch定理

Algebraic cycles on fiber bundles of Leray-Hirsch type

We give a theorem of Leray-Hirsch type for Chow groups and use it to study the Hogde and Grothendieck's standard conjectures for algebraic fiber bundles of Leray-Hirsch type. Morevoer, the Hodge conjecture for product varieties will also be considered.

关于纯塔利纤维束的motivic Leray-Hirsch定理

On The Motivic Leray-Hirsch Theorem For Pure Tate Fibre Bundles

本文在Chow动机范畴中证明了纯塔利纤维束的motivic Leray-Hirsch定理，并探讨了其应用。

Invariance of Quantum Rings under Ordinary Flops II: A quantum Leray--Hirsch theorem

This is the second of a sequence of papers proving the quantum invariance for ordinary flops over an arbitrary smooth base. In this paper, we complete the proof of the invariance of the big quantum rings under ordinary flops of splitting type. To achieve that, several new ingredients are introduced. One is a quantum Leray--Hirsch theorem for the local model (a certain toric bundle) which extends the quantum D module of Dubrovin connection on the base by a Picard--Fuchs system of the toric fibers. Nonsplit flops as well as further applications of the quantum Leray--Hirsch theorem will be discus…

Leray-Hirsch theorem and blow-up formula for Dolbeault cohomology

We prove a theorem of Leray-Hirsch type and give an explicit blow-up formula for Dolbeault cohomology on (\emph{not necessarily compact}) complex manifolds. We give applications to strongly $q$-complete manifolds and the $\partial\bar{\partial}$-lemma.

A quantum Leray-Hirsch theorem for banded gerbes

For a gerbe $\Y$ over a smooth proper Deligne-Mumford stack $\B$ banded by a finite group $G$, we prove a structure result on the Gromov-Witten theory of $\Y$, expressing Gromov-Witten invariants of $\Y$ in terms of Gromov-Witten invariants of $\B$ twisted by various flat $U(1)$-gerbes on $\B$. This is interpreted as a Leray-Hirsch type of result for Gromov-Witten theory of gerbes.

Borel (α,β)-多重变换与量子 Leray-Hirsch：Fano 簇上 $\mathbb P^1$-丛的量子微分方程解的积分表示

Borel $(α,β)$-multitransforms and Quantum Leray-Hirsch: integral representations of solutions of quantum differential equations for $\mathbb P^1$-bundles

本文利用 Borel (α,β)-多重变换，从底空间的量子微分方程解重构 $\mathbb P^1$-丛全空间的解，建立了量子 Leray-Hirsch 定理，并给出 Mellin-Barnes 积分表示及爆破情形的应用。