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Xiaolei Zhao

Publications and source records attributed to Xiaolei Zhao.

At least 19 recordsLinked to original sources
arXiv2026

Stability conditions and moduli spaces on projective families

We extend the construction of stability conditions on projective schemes over a field to projective families over an arbitrary base, and prove that they admit proper relative moduli spaces of semistable objects. We also prove a number of complementary results: the existence of mass-Hom bounds for these stability conditions, as conjectured by Halpern-Leistner and Robotis; a comparison with tilt-stability on surfaces and threefolds; a construction of stability conditions on the supported derived category of total spaces of certain vector bundles, including all local Calabi--Yau varieties; and a simple new proof of Bondal and Orlov's reconstruction theorem.

math.AG↗
arXiv2025

Stability conditions on products of curves and Hilbert schemes of surfaces

We prove that stability conditions on the derived category of a product of curves of positive genus are uniquely determined by their central charge and the phase of skyscraper sheaves. As an application, we construct stability conditions on Hilbert schemes of points on certain surfaces, including some K3 surfaces of Kummer type.

math.AG↗
arXiv2025

Exploration on Real World Assets and Tokenization

This study delves into the tokenization of real-world assets (RWAs) on the blockchain with the objective of augmenting liquidity and refining asset management practices. By conducting an exhaustive analysis of the technical procedures implicated and scrutinizing case studies of existing deployments, this research evaluates the advantages, hurdles, and prospective advancements of blockchain technology in reshaping conventional asset management paradigms.

cs.CR↗
arXiv2025

Derived categories of quartic double fivefolds

We construct singular quartic double fivefolds whose Kuznetsov component admits a crepant categorical resolution of singularities by a twisted Calabi--Yau threefold. We also construct rational specializations of these fivefolds where such a resolution exists without a twist. This confirms an instance of a higher-dimensional version of Kuznetsov's rationality conjecture, and of a noncommutative version of Reid's fantasy on the connectedness of the moduli of Calabi--Yau threefolds.

math.AG↗
arXiv2024

Higher dimensional moduli spaces on Kuznetsov components of Fano threefolds

We study moduli spaces of stable objects in the Kuznetsov components of Fano threefolds. We prove a general non-emptiness criterion for moduli spaces, which applies to the cases of prime Fano threefolds of index $1$, degree $10 \leq d \leq 18$, and index $2$, degree $d \leq 4$. In the second part, we focus on cubic threefolds. We show the irreducibility of the moduli spaces, and that the general fibers of the Abel--Jacobi maps from the moduli spaces to the intermediate Jacobian are Fano varieties. When the dimension is sufficiently large, we further show that the general fibers of the Abel--Jacobi maps are stably birational equivalent to each other. As an application of our methods, we prove Conjecture A.1 in [FGLZ24] concerning the existence of Lagrangian subvarieties in moduli spaces of stable objects in the Kuznetsov components of very general cubic fourfolds.

math.AG↗
arXiv2024

Fully faithful functors, skyscraper sheaves, and birational equivalence

Let $X$ and $Y$ be two smooth projective varieties such that there is a fully faithful exact functor from $D^b(\mathrm{Coh}(X))$ to $D^b(\mathrm{Coh}(Y))$. We show that $X$ and $Y$ are birational equivalent if the functor maps one skyscraper sheaf to a skyscraper sheaf. Further assuming that $X$ and $Y$ are of the same dimension, we show that if $X$ has ample canonical bundle and $H^0(X ,K_X)\neq 0$, or if $X$ is a K3 surface with Picard number one, then $Y$ is birational to a Fourier--Mukai partner of $X$.

math.AG↗
arXiv2024

Some remarks about deformation theory and formality conjecture

Using the algebraic criterion proved by Bandiera, Manetti and Meazzini, we show the formality conjecture for universally gluable objects with linearly reductive automorphism groups in the bounded derived category of a K3 surface. As an application, we prove the formality conjecture for polystable objects in the Kuznetsov components of Gushel--Mukai threefolds and quartic double solids.

math.AG↗
arXiv2023

Moduli spaces of stable objects in Enriques categories

We study moduli spaces of stable objects in Enriques categories by exploiting their relation to moduli spaces of stable objects in associated K3 categories. In particular, we settle the nonemptiness problem for moduli spaces of stable objects in the Kuznetsov components of several interesting classes of Fano varieties, and deduce the nonemptiness of fixed loci of certain antisymplectic involutions on modular hyperkähler varieties.

math.AG↗
arXiv2023

Stability conditions and moduli spaces for Kuznetsov components of Gushel-Mukai varieties

We prove the existence of Bridgeland stability conditions on the Kuznetsov components of Gushel-Mukai varieties, and describe the structure of moduli spaces of Bridgeland semistable objects in these categories in the even-dimensional case. As applications, we construct a new infinite series of unirational locally complete families of polarized hyperkähler varieties of K3 type, and characterize Hodge-theoretically when the Kuznetsov component of an even-dimensional Gushel-Mukai variety is equivalent to the derived category of a K3 surface.

math.AG↗
arXiv2022

Derived categories of hearts on Kuznetsov components

We prove a general criterion which guarantees that an admissible subcategory $\mathcal{K}$ of the derived category of an abelian category is equivalent to the bounded derived category of the heart of a bounded t-structure. As a consequence, we show that $\mathcal{K}$ has a strongly unique dg enhancement, applying the recent results of Canonaco, Neeman and Stellari. We apply this criterion to the Kuznetsov component $\mathop{\mathcal{K}u}(X)$ when $X$ is a cubic fourfold, a Gushel--Mukai variety or a quartic double solid. In particular, we obtain that these Kuznetsov components have strongly unique dg enhancement and that exact equivalences of the form $\mathop{\mathcal{K}u}(X) \xrightarrow{\sim} \mathop{\mathcal{K}u}(X')$ are of Fourier--Mukai type when $X$, $X'$ belong to these classes of varieties, as predicted by a conjecture of Kuznetsov.

math.AG↗
arXiv2022

Stability manifolds of varieties with finite Albanese morphisms

For a smooth projective complex variety whose Albanese morphism is finite, we show that every Bridgeland stability condition on its bounded derived category of coherent sheaves is geometric, in the sense that all skyscraper sheaves are stable with the same phase. Furthermore, we describe the stability manifolds of irregular surfaces and abelian threefolds with Picard rank one, and show that they are connected and contractible.

math.AG↗
arXiv2021

$^{210}$Pb measurements at the André E. Lalonde AMS Laboratory for the radioassay of materials used in rare event search detectors

Naturally occurring radionuclide $^{210}$Pb ($T_{1/2}$=22.2 y) is an important source of background in rare event searches, such as neutrinoless double-$β$ decay and dark matter direct detection experiments. When a sample mass of hundreds of grams is available, $γ$-counting measurements can be performed. However, there are other cases where only grams of sample can be used. For these cases, better sensitivities are required. In this paper, in collaboration with the Astroparticle Physics group at Carleton University, the capabilities of the A.E. Lalonde AMS Laboratory at the University of Ottawa for $^{210}$Pb measurements are discussed. PbF$_{2}$ and PbO targets were used, selecting in the low energy sector, respectively, (PbF$_{3}$)$^{-}$ or (PbO$_{2}$)$^{-}$ ions. For fluoride targets, the blank $^{210}$Pb/$^{206}$Pb ratio was in the 10$^{-14}$ to 10$^{-13}$ range, but current output was lower and less stable. For oxide targets, current output showed better stability, despite a significant difference in current output for commercial PbO and processed samples, and background studies suggested a background not much higher than that of the fluoride targets. Both target materials showed, therefore, good performance for $^{210}$Pb AMS assay. Measurements of Kapton films, an ultra-thin polymer material, where masses available are typically just several grams, were performed. 90% C.L. upper limits for the $^{210}$Pb specific activity in the range of 0.74-2.8 Bq/kg were established for several Kapton HN films.

physics.ins-det↗
arXiv2020

A refined Derived Torelli Theorem for Enriques surfaces

We prove that two general Enriques surfaces defined over an algebraically closed field of characteristic different from $2$ are isomorphic if their Kuznetsov components are equivalent. We apply the same techniques to give a new simple proof of a conjecture by Ingalls and Kuznetsov relating the derived categories of the blow-up of general Artin\textendash Mumford quartic double solids and of the associated Enriques surfaces. This paper originated from one of the problem sections at the workshop \emph{Semiorthogonal decompositions, stability conditions and sheaves of categories}, Université de Toulouse, May 2--5, 2018.

math.AG↗
arXiv2020

Twisted cubics on cubic fourfolds and stability conditions

We give an interpretation of the Fano variety of lines on a cubic fourfold and of the hyperkahler eightfold, constructed by Lehn, Lehn, Sorger and van Straten from twisted cubic curves in a cubic fourfold non containing a plane, as moduli spaces of Bridgeland stable objects in the Kuznetsov component. As a consequence, we reprove the categorical version of Torelli Theorem for cubic fourfolds, we obtain the identification of the period point of LLSvS eightfold with that of the Fano variety, and we discuss derived Torelli Theorem for cubic fourfolds.

math.AG↗
arXiv2020

Elliptic quintics on cubic fourfolds, O'Grady 10, and Lagrangian fibrations

For a smooth cubic fourfold Y, we study the moduli space M of semistable objects of Mukai vector $2λ_1+2λ_2$ in the Kuznetsov component of Y. We show that with a certain choice of stability conditions, M admits a symplectic resolution $\tilde M$, which is a smooth projective hyperkähler manifold, deformation equivalent to the 10-dimensional examples constructed by O'Grady. As applications, we show that a birational model of $\tilde M$ provides a hyperkähler compactification of the twisted family of intermediate Jacobians associated to Y. This generalizes the previous result of Voisin arXiv:1611.06679 in the very general case. We also prove that $\tilde M$ is the MRC quotient of the main component of the Hilbert scheme of elliptic quintic curves in Y, confirming a conjecture of Castravet.

math.AG↗