arXiv subjects

Eduardo González

Publications and source records attributed to Eduardo González.

3 recordsLinked to original sources

arXiv2026

Nef Hattori classes and products of projective lines

Let $X$ be a smooth connected complex projective variety with an effective algebraic $\mathbb C^{\times}$-action, a nonempty finite fixed locus whose weights are $\pm1$. We show that if its Hattori line bundles are nef, then $X$ is algebraically isomorphic to $(\mathbb{P}^1)^{\dim X}$, and these bundles become the hyperplane bundles of the factors. The product statement follows from the nef-complexity classification of Enwright and collaborators, and we describe the isomorphism through global sections. To test the required nefness we specialise the orbit-graph criterion of Romano and Wiśniewski. The Hirzebruch surface $\mathbb F_2$ is an example why the topological hypotheses alone do not imply either the product conclusion or the Fano property.

math.AG↗

arXiv2022

Affine nil-Hecke algebras and Quantum cohomology

Let $G$ be a compact, connected Lie group and $T \subset G$ a maximal torus. Let $(M,ω)$ be a monotone closed symplectic manifold equipped with a Hamiltonian action of $G$. We construct a module action of the affine nil-Hecke algebra $\hat{H}_*^{S^1 \times T}(LG/T)$ on the $S^1 \times T$-equivariant quantum cohomology of $M$, $QH^*_{S^1 \times T}(M).$ Our construction generalizes the theory of shift operators for Hamiltonian torus actions [OP,LJ]. We show that, as in the abelian case, this action behaves well with respect to the quantum connection. As an application of our construction, we show that when $G$ is semi-simple, the $G$-equivariant quantum cohomology $QH_G^*(M)$ defines a canonical holomorphic Lagrangian subvariety $\mathbb{L}_G(M) \hookrightarrow BFM(G_{\mathbb{C}}^{\vee})$ in the BFM-space of the Langlands dual group, confirming an expectation of Teleman from [T1].

math.SG↗

arXiv2022

Quantum Kirwan for quantum K-theory

For G a complex reductive group and X a smooth projective or convex quasi-projective polarized G-variety we construct a formal map in quantum K-theory from the equivariant quantum K-theory $QK^G(X)$ to the quantum K-theory of the git quotient $QK(X//G)$ assuming the quotient $X//G$ is a smooth Deligne-Mumford stack with projective coarse moduli space. As an example, we give a presentation of the (possibly bulk-shifted) quantum K-theory of any smooth proper toric Deligne-Mumford stack with projective coarse moduli space. We also provide awall-crossing formula for the K-theoretic gauged potential under variation of git quotient, a proof of the invariance of certain K-theoretic Gromov-Witten invariants under (strong) crepant transformation assumptions, and a proof of a version of the abelian non-abelian correspondence.

math.AG↗