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Jennifer Li

Publications and source records attributed to Jennifer Li.

12 recordsLinked to original sources
arXiv2026

Weighted projective degenerations of $\mathbb{P}^{n}$

We study weighted projective klt $\mathbb{Q}$-Gorenstein degenerations of projective space $\mathbb{P}^{n}$ and construct infinitely many new degenerations of projective space in any dimension. We also study in detail the deformations of arbitrary weighted projective threefolds. The rest of the paper provides several applications of the existence of degenerations of $\mathbb{P}^{n}$ and our methods apply to find many degenerations of $\mathbb{P}^{n}$ beyond just weighted projective spaces.

math.AG↗
arXiv2026

Deformations of fibered Calabi--Yau varieties

Koll\'{a}r showed that small deformations of elliptically fibered smooth $K$-torsion varieties with $H^2(X,\mathcal{O}_X)=0$ remain elliptically fibered. We extend this result to any fibered smooth $K$-torsion variety $X$ with $H^2(X,\mathcal{O}_X)=0$, using Hodge theoretic techniques and the $T^1$-lifting criterion of Kawamata--Ran. More generally, our strategy implies that even without the cohomological assumption, small deformations of a semiample line bundle on a smooth $K$-torsion variety remain semiample up to homological equivalence.

math.AG↗
arXiv2026

SELDON: Supernova Explosions Learned by Deep ODE Networks

The discovery rate of optical transients will explode to 10 million public alerts per night once the Vera C. Rubin Observatory's Legacy Survey of Space and Time comes online, overwhelming the traditional physics-based inference pipelines. A continuous-time forecasting AI model is of interest because it can deliver millisecond-scale inference for thousands of objects per day, whereas legacy MCMC codes need hours per object. In this paper, we propose SELDON, a new continuous-time variational autoencoder for panels of sparse and irregularly time-sampled (gappy) astrophysical light curves that are nonstationary, heteroscedastic, and inherently dependent. SELDON combines a masked GRU-ODE encoder with a latent neural ODE propagator and an interpretable Gaussian-basis decoder. The encoder learns to summarize panels of imbalanced and correlated data even when only a handful of points are observed. The neural ODE then integrates this hidden state forward in continuous time, extrapolating to future unseen epochs. This extrapolated time series is further encoded by deep sets to a latent distribution that is decoded to a weighted sum of Gaussian basis functions, the parameters of which are physically meaningful. Such parameters (e.g., rise time, decay rate, peak flux) directly drive downstream prioritization of spectroscopic follow-up for astrophysical surveys. Beyond astronomy, the architecture of SELDON offers a generic recipe for interpretable and continuous-time sequence modeling in any time domain where data are multivariate, sparse, heteroscedastic, and irregularly spaced.

astro-ph.IM↗
arXiv2025

Weighted surfaces with maximal Picard number

An algorithm due to Shioda computes the Picard number for certain surfaces which are defined by a single equation with exactly four monomials, called Delsarte surfaces. We consider this method for surfaces in weighted projective $3$-space with quotient singularities. We give a criterion for such a weighted Delsarte surface $X$ to have maximal Picard number. This condition is surprisingly related to the automorphism group of $X$. For every positive integer $s$, we find a weighted Delsarte surface with geometric genus $s$ and maximal Picard number. We show that these examples are elliptic surfaces, proving that elliptic surfaces of maximal Picard number and arbitrary geometric genus may be embedded as quasismooth hypersurfaces in weighted projective space.

math.AG↗
arXiv2025

Complexity one varieties are cluster type

The complexity of a Calabi-Yau pair $(X,B)$ is an invariant that relates the dimension of $X$, the rank of the group of divisors, and the coefficients of $B$. If the complexity is less than one, then $X$ is a toric variety. We prove that if the complexity is less than two, then $X$ is a Fano type variety. Furthermore, if the complexity is less than 3/2, then $X$ admits a Calabi-Yau structure of complexity one and index at most two, and it admits a finite cover $Y \to X$ of degree at most 2, where $Y$ is a cluster type variety. In particular, if the complexity is one and the index is one, $(X,B)$ is cluster type. Finally, we establish a connection with the theory of $T$-varieties. We prove that a variety of $T$-complexity one admits a similar finite cover from a cluster type variety.

math.AG↗
arXiv2024

Hypersurfaces with large automorphism groups

We find sharp upper bounds on the order of the automorphism group of a hypersurface in complex projective space in every dimension and degree. In each case, we prove that the hypersurface realizing the upper bound is unique up to isomorphism and provide explicit generators for the automorphism group.

math.AG↗
arXiv2023

Rational surfaces with a non-arithmetic automorphism group

In arXiv:1008.3825, Totaro gave examples of a K3 surface such that its automorphism group is not commensurable with an arithmetic group, answering a question of Mazur. We give examples of rational surfaces with the same property. Our examples $Y$ are Looijenga pairs, i.e., there is a connected singular nodal curve $D \subset Y$ such that $K_{Y} + D = 0$.

math.AG↗
arXiv2023

On the cone conjecture for log Calabi-Yau mirrors of Fano 3-folds

Let $Y$ be a smooth projective $3$-fold admitting a K3 fibration $f : Y \rightarrow \mathbb{P}^1$ with $-K_Y = f^*\mathcal{O}(1)$. We show that the pseudoautomorphism group of $Y$ acts with finitely many orbits on the codimension one faces of the movable cone if $H^3(Y,\mathbb{C})=0$, confirming a special case of the Kawamata--Morrison--Totaro cone conjecture. In [CCGK16], [P18], and [CP18], the authors construct log Calabi-Yau 3-folds with K3 fibrations satisfying the hypotheses of our theorem as the mirrors of Fano 3-folds.

math.AG↗
arXiv2022

A cone conjecture for log Calabi-Yau surfaces

We consider log Calabi-Yau surfaces $(Y, D)$ with singular boundary. In each deformation type, there is a distinguished surface $(Y_e,D_e)$ such that the mixed Hodge structure on $H_2(Y \setminus D)$ is split. We prove that (1) the action of the automorphism group of $(Y_e,D_e)$ on its nef effective cone admits a rational polyhedral fundamental domain; and (2) the action of the monodromy group on the nef effective cone of a very general surface in the deformation type admits a rational polyhedral fundamental domain. These statements can be viewed as versions of the Morrison cone conjecture for log Calabi--Yau surfaces. In addition, if the number of components of $D$ is $\le 6$, we show that the nef cone of $Y_e$ is rational polyhedral and describe it explicitly. This provides infinite series of new examples of Mori Dream Spaces.

math.AG↗
arXiv2022

Non-symplectic automorphisms of order multiple of seven on K3 surfaces

In this paper we present a classification of non-symplectic automorphisms of K3 surfaces whose order is a multiple of seven by describing the topological type of their fixed locus. In the case of purely non-symplectic automorphisms, we provide new results for order 14 and alternative proofs for orders 21, 28 and 42, so that we can unify in the same paper the results on these automorphisms. For each of these orders we also consider not purely non-symplectic automorphisms and obtain a complete characterization of their fixed loci. Several results of our paper were obtained independently in a recent paper by Brandhorst and Hofmann, but the methods used in the two papers are completely different.

math.AG↗
arXiv2019

The Sloan Digital Sky Survey Reverberation Mapping Project: Improving Lag Detection with an Extended Multi-Year Baseline

We investigate the effects of extended multi-year light curves (9-year photometry and 5-year spectroscopy) on the detection of time lags between the continuum variability and broad-line response of quasars at z>~1.5, and compare with the results using 4-year photometry+spectroscopy presented in a companion paper. We demonstrate the benefits of the extended light curves in three cases: (1) lags that are too long to be detected by the shorter-duration data but can be detected with the extended data; (2) lags that are recovered by the extended light curves but missed in the shorter-duration data due to insufficient light curve quality; and (3) lags for different broad line species in the same object. These examples demonstrate the importance of long-term monitoring for reverberation mapping to detect lags for luminous quasars at high-redshift, and the expected performance of the final dataset from the Sloan Digital Sky Survey Reverberation Mapping project that will have 11-year photometric and 7-year spectroscopic baselines.

astro-ph.GA↗