arXiv subjects

Ban Lin

Publications and source records attributed to Ban Lin.

4 recordsLinked to original sources

arXiv2026

GLSM monodromy on quantum period lattice of Calabi-Yau fourfold flops

We establish an integral basis for the B-brane central charges of certain Calabi-Yau fourfold flops and derive exact expressions for their monodromies using the grade restriction rule and window categories of the associated gauged linear sigma models. The monodromy is interpreted as an EZ twist associated with the contraction of an exceptional surface onto a curve of conifold singularities. We further illustrate a decomposition of the EZ twist into spherical twists for families of splitting configurations of the sixtic Calabi-Yau fourfold and a complete intersection in grassmannian.

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arXiv2026

Monodromy of Calabi-Yau threefold flops via grade restriction rule and their quantum Kahler moduli

We present exact expressions, based on the grade restriction rule and window categories, for monodromies associated to certain Calabi-Yau threefold flops. We show a general formula for the monodromy action on the lattice of B-brane charges, based on the hemisphere partition function for abelian and nonabelian gauged linear sigma models. We exploit the explicit form of the discriminant in the quantum K\"ahler moduli to further refine the form of the monodromies, in several examples, using their relation to the fundamental group of nested torus links.

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arXiv2024

B-brane Transport and Grade Restriction Rule for Determinantal Varieties

We study autoequivalences of $D^{b}Coh(X)$ associated to B-brane transport around loops in the stringy K\"ahler moduli of $X$. We consider the case of $X$ being certain resolutions of determinantal varieties embedded in $\mathbb{P}^{d}\times G(k,n)$. Such resolutions have been modeled, in general, by nonabelian gauged linear sigma models (GLSM). We use the GLSM construction to determine the window categories associated with B-brane transport between different geometric phases using the machinery of grade restriction rule and the hemisphere partition function. In the family of examples analyzed the monodromies around phase boundaries enjoy the interpretation as loop inside link complements. We exploit this interpretation to find a decomposition of autoequivalences into simpler spherical functors and we illustrate this in two examples of Calabi-Yau 3-folds $X$, modeled by an abelian and nonabelian GLSM respectively. In additon we also determine explicitly the action of the autoequivalences on the Grothendieck group $K(X)$ (or equivalently, B-brane charges).

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arXiv2023

A GLSM realization of derived equivalence in $U(1) \times U(2)$ models

This paper studies the derived equivalence between Calabi--Yau mixed branches using the B-brane hemisphere partition function in anomalous gauged linear sigma models (GLSMs). For a family of anomalous $U(2)$ GLSMs, we study the infrared behavior of B-branes under RG flow and the variation of FI parameters in the quantum K\"ahler moduli space. As characterized by the big and small window categories of the GLSM, the RG flow effect is analyzed according to the properties of their B-brane central charges as hemisphere partition functions. The result generalizes the band restriction rules in anomalous abelian GLSMs (Clingempeel--Floch--Romo) to some $U(2)$ models. As an application, we study a family of $U(1)\times U(k)$ models for $k=1,2$, which realize a Fano UV sigma model and two IR phases as mixed branches accompanied by local Calabi--Yau Higgs components. By applying the restriction rules, we establish new derived equivalences between Calabi--Yau varieties from these anomalous models.

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