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Wei-Ping Li

Publications and source records attributed to Wei-Ping Li.

At least 19 recordsLinked to original sources
arXiv2026

Stability conditions in the mathematical Gauged Linear Sigma Model

The theory of Mixed-Spin-P (MSP) fields was introduced by Chang-Li-Li-Liu for the quintic threefold, aiming at studying its higher-genus Gromov-Witten invariants. Chang-Guo-Li has successfully applied it to prove conjectures including the BCOV Feynman rule, Yamaguchi-Yau's polynomiality conjecture and the Holomorphic Anomaly Equation. Meanwhile, Fan-Jarvis-Ruan introduced a mathematical theory of Gauged Linear Sigma Model (GLSM), associating a counting theory to a GIT quotient with a super-potential, under suitable assumptions. This paper provides a common generalization of both works, by introducing new stability conditions in the mathematical GLSM. We show that our stability condition guarantees the separatedness and properness of the cosection degeneracy locus in the moduli. It generalizes the MSP fields construction to more general GIT quotients, including Calabi-Yau global complete intersections in toric varieties. This hopefully provides a geometric platform to effectively compute their higher-genus Gromov-Witten invariants.

math.AG↗
arXiv2026

A boundedness theorem for principal bundles on curves

Let $G$ be a reductive group acting on an affine scheme $V$. We study the set of principal $G$-bundles on a smooth projective curve $\mathcal C$ such that the associated $V$-bundle admits a section sending the generic point of $\mathcal C$ into the GIT stable locus $V^{\mathrm{s}}(θ)$. We show that after fixing the degree of the line bundle induced by the character $θ$, the set of such principal $G$-bundles is bounded. The statement of our theorem is made slightly more general so that we deduce from it the boundedness for $ε$-stable quasimaps and $Ω$-stable LG-quasimap.

math.AG↗
arXiv2025

Instantons on the Blown-up Surface and the Affine Vertex Algebra

We answer a long-standing question raised by Vafa--Witten on a relation between S-duality and conformal field theory, which related Yoshioka's blow-up formula and the WZW model for $\mathrm{SU}(r)$ at level $1$. Precisely, for the moduli space of Euler characteristics of rank $r$ instantons on the blow-up of an algebraic surface along a closed point, we construct the affine $\mathrm{gl}_r$-action on various cohomology theories, including the Grothendieck group of coherent sheaves, Hochschild homology groups, Chow groups and Hodge cohomology groups, and identifying the module as a basic representation. A key ingredient in our proof is a representation-theoretic reformulation of the theory of Grassmannians of Tor-amplitude $[0,1]$-perfect complexes studied by the first-named author in terms of the spin representation of the finite-dimensional Clifford algebra. This may be viewed as a finite analog of the question of Vafa--Witten via the Boson--Fermion correspondence.

math.AG↗
arXiv2022

Mobile defects as mediated states for charge-carrier trapping in metal halide perovskites quantum dots

The migration motion of defects in metal halide perovskites quantum dots (MHPQDs) results in charge-carrier trapping become more complicated. We study two-step trapping mediated by mobile defects between the ground state of MHPQDs and a fixed-depth defect using a full-configuration defect method, where all possible trapping processes mediated by these mobile defects could be reproduced and the fastest channels among them are picked out. We find that these two-step trapping processes could keep more one order of magnitude faster than these direct ones as mobile defect with the appropriate localization strength, which implies that these indirect trapping should play the crucial rule to determine the non-radiative recombination losses. These results provide the significant explanation for studying non-radiation processes of carriers in the presence of the migration defects in recent experiments. Moreover, this model will be available to analyze some key performance related defects in electronic devices.

cond-mat.mes-hall↗
arXiv2020

A genus-one FJRW invariant via two methods

We calculate a genus-one FJRW invariant of an LG pair $(W_3=x_1^3+x_2^3+x_3^3, μ_3)$ via two different methods. In the first method, we apply the cosection localization technique to get a genus-one three-spin virtual class explicitly and then calculate the target FJRW invariant via self-intersections of the three-spin virtual class. In the second method, we apply the Mixed Spin P-fields method for the pair and calculate the invariant using the localization formula. This invariant is the building block in establishing the all-genera LG/CY correspondence and its determination enables one to compute the all-genera FJRW invariants for the LG pair.

math.AG↗
arXiv2019

The theory of N-Mixed-Spin-P fields

This is the first part of the project toward proving the BCOV's Feymann graph sum formula of all genera Gromov-Witten invariants of quintic Calabi-Yau threefolds. In this paper, we introduce the notion of N-Mixed-Spin-P fields, construct their moduli spaces, their virtual cycles, their virtual localization formulas, and a vanishing result associated with irregular graphs.

math.AG↗
arXiv2019

On the mathematics and physics of Mixed Spin P-Fields

We outline various developments of affine and general Landau Ginzburg models in physics. We then describe the A-twisting and coupling to gravity in terms of Algebraic Geometry. We describe constructions of various path integral measures (virtual fundamental class) using the algebro-geometric technique of cosection localization, culminating in the theory of ``Mixed Spin P (MSP) fields" developed by the authors.

math.AG↗
arXiv2017

Genus one GW invariants of quintic threefolds via MSP localization

The moduli stack of Mixed Spin P-fields (MSP) provides an effective algorithm to evaluate all genus Gromov-Witten invariants of quintic Calabi-Yau threefolds. This paper is to apply the algorithm in genus one case. We use the localization formula, the proposed algorithm in [CLLL1, CLLL2], and Zinger's packaging technique to compute the genus one Gromov-Witten invariants of quintic Calabi-Yau threefolds. New hypergeometric series identities are also discovered in the process.

math.AG↗
arXiv2017

Correction of exciton binding energy in monolayer transition metal dichalcogenides

We theoretically investigate the corrections of exciton binding energy in monolayer transition metal dichalcogenides (TMDs) due to the exciton-optical phonon coupling in the Fr$\ddot{o}$hlich interaction model by using the linear operator combined Lee-Low-Pines variational method. We not only consider the excitons couple with the intrinsic longitudinal optical (LO) phonon modes, but also the surface optical phonon modes that induced by the polar substrates underneath the TMDs. We find that exciton binding energies are corrected in a large scale due to these exciton-optical phonon couplings. We discuss the dependences of exciton binding energy on the cut-off wave vector of optical phonon modes, the polarization parameters of materials and the interlayer distance between the polar substrates and TMDs. These results provide potential explanations for the divergence of the exciton binding energy between experiment and theory in TMDs.

cond-mat.mes-hall↗
arXiv2016

A survey on mixed spin P-fields

This is a survey on the mixed spin P-fields (MSP fields for short) theory which provides a platform to understand the phase transition between Gromov-Witten theory of quintic CY 3-folds and Landau-Ginzburg theory of the corresponding quintic polynomials. It discusses key ideas that lead to the definition of MSP fields and how moduli of stable maps to the quintic and that of 5-spin curves appear in the moduli of MSP fields. It also explains some properties of the moduli of MSP fields such as the cosection localisation, the properness of the degeneracy locus, and a torus action on the moduli.. Some vanishings arising from the torus action provide polynomial relations among GW-invarants and FJRW-invaraints which give an effective algorithm for the computation of those invariants. Some examples of computations of genus 1 low degree of GW invariants are provided.

math.AG↗
arXiv2015

Mixed-Spin-P fields of Fermat quintic polynomials

This is the first part of the project toward an effective algorithm to evaluate all genus Gromov-Witten invariants of quintic Calabi-Yau threefolds. In this paper, we introduce the notion of Mixed-Spin-P fields, construct their moduli spaces, and construct the virtual cycles of these moduli spaces.

math.AG↗
arXiv2014

The Gromov-Witten invariants of the Hilbert schemes of points on surfaces with $p_g > 0$

In this paper, we study the Gromov-Witten theory of the Hilbert schemes X^{[n]} of points on smooth projective surfaces X with positive geometric genus p_g. Using cosection localization technique due to Y. Kiem and J. Li [KL1, KL2], we prove that if X is a simply connected surface admitting a holomorphic differential two-form with irreducible zero divisor, then all the Gromov-Witten invariants of X^{[n]} defined via the moduli space $\Mbar_{g, r}(X^{[n]}, β)$ vanish except possibly when $β= d_0 β_{K_X} - d β_n$ where d is an integer, $d_0 \ge 0$ is a rational number, and $β_n$ and $β_{K_X}$ are defined in (3.2) and (3.3) respectively. When $n=2$, the exceptional cases can be further reduced to the invariants: $<1>_{0, β_{K_X} - dβ_2}^{X^{[2]}}$ with $K_X^2 = 1$ and $d \le 3$, and $<1>_{1, dβ_2}^{X^{[2]}}$ with $d \ge 1$. We show that when $K_X^2 = 1$, $$<1>_{0, β_{K_X} - 3 β_2}^{X^{[2]}} = (-1)^{χ(\mathcal O_X)}$$ which is consistent with a well-known formula of Taubes [Tau]. In addition, for an arbitrary smooth projective surface X and $d \ge 1$, we verify that $$<1>_{1, dβ_2}^{X^{[2]}} = K_X^2/(12d).$$

math.AG↗
arXiv2013

The Cohomological Crepant Resolution Conjecture for the Hilbert-Chow morphisms

In this paper, we prove that Ruan's Cohomological Crepant Resolution Conjecture holds for the Hilbert-Chow morphisms. There are two main ideas in the proof. The first one is to use the representation theoretic approach proposed in [QW] which involves vertex operator techniques. The second is to prove certain universality structures about the 3-pointed genus-0 extremal Gromov-Witten invariants of the Hilbert schemes by using the indexing techniques from [LiJ], the product formula from [Beh2] and the co-section localization from [KL1, KL2, LL]. We then reduce Ruan's Conjecture from the case of an arbitrary surface to the case of smooth projective toric surfaces which has already been proved in [Che].

math.AG↗
arXiv2013

Witten's top Chern class via cosection localization

For a Landau Ginzburg space ([C^n/G],W), we construct the Witten's top Chern classes as algebraic cycles via cosection localized virtual cycles in case all sectors are narrow. We verify all axioms of such classes. We derive an explicit formula of such classes in the free case. We prove that this construction is equivalent to the prior constructions of Polishchuk-Vaintrob, of Chiodo and of Fan-Jarvis-Ruan.

math.AG↗
arXiv2010

Donaldson-Thomas invariants of certain Calabi-Yau 3-folds

We compute the Donaldson-Thomas invariants for two types of Calabi-Yau 3-folds. These invariants are associated to the moduli spaces of rank-2 Gieseker semistable sheaves. None of the sheaves are locally free, and their double duals are locally free stable sheaves investigated earlier by Donaldson and Thomas, Li and Qin respectively. We show that these Gieseker moduli spaces are isomorphic to some Quot-schemes. We prove a formula for Behrend's functions when torus actions present with positive dimensional fixed point sets, and use it to obtain the generating series of the relevant Donaldson-Thomas invariants in terms of the McMahon function. Our results might shed some light on the wall-crossing phenomena of Donaldson-Thomas invariants.

math.AG↗
arXiv2009

1-point Gromov-Witten invariants of the moduli spaces of sheaves over the projective plane

The Gieseker-Uhlenbeck morphism maps the Gieseker moduli space of stable rank-2 sheaves on a smooth projective surface to the Uhlenbeck compactification, and is a generalization of the Hilbert-Chow morphism for Hilbert schemes of points. When the surface is the complex projective plane, we determine all the 1-point genus-0 Gromov-Witten invariants extremal with respect to the Gieseker-Uhlenbeck morphism. The main idea is to understand the virtual fundamental class of the moduli space of stable maps by studying the obstruction sheaf and using a meromorphic 2-form on the Gieseker moduli space.

math.AG↗
arXiv2008

Equivariant cohomology of incidence Hilbert schemes and loop algebras

Let $S$ be the affine plane $\C^2$ together with an appropriate $\mathbb T = \C^*$ action. Let $\hil{m,m+1}$ be the incidence Hilbert scheme. Parallel to \cite{LQ}, we construct an infinite dimensional Lie algebra that acts on the direct sum $$\Wft = \bigoplus_{m=0}^{+\infty}H^{2(m+1)}_{\mathbb T}(S^{[m,m+1]})$$ of the middle-degree equivariant cohomology group of $\hil{m,m+1}$. The algebra is related to the loop algebra of an infinite dimensional Heisenberg algebra. In addition, we study the transformations among three different linear bases of $\Wft$. Our results are applied to the ring structure of the ordinary cohomology of $\hil{m,m+1}$ and to the ring of symmetric functions in infinitely many variables.

math.AG↗