Kristin DeVleming

About

Kristin DeVleming is an assistant professor in the UCSD Math Department specializing in algebraic geometry. Prior to her current position at UCSD, she served as an assistant professor at UMass Amherst. Her research focuses on various aspects of algebraic geometry, and further details about her work can be found on the research section of her professional webpage. In addition to her academic pursuits, she is known to have a personal interest in animals, particularly dogs and cats, and enjoys engaging with students who share photos of their pets.

Research topics

• Physics
• Geometry
• Pure mathematics
• Mathematics
• Quantum mechanics
• Algorithm
• Mathematical analysis

Selected publications

• Wall crossing for K-moduli spaces of plane curves

  arXiv (Cornell University) · 2019-09-10 · 20 citations

  preprintOpen access

  We construct proper good moduli spaces parametrizing K-polystable $\mathbb{Q}$-Gorenstein smoothable log Fano pairs $(X, cD)$, where $X$ is a Fano variety and $D$ is a rational multiple of the anti-canonical divisor. We then establish a wall-crossing framework of these K-moduli spaces as $c$ varies. The main application in this paper is the case of plane curves of degree $d \geq 4$ as boundary divisors of $\mathbb{P}^2$. In this case, we show that when the coefficient $c$ is small, the K-moduli…

  PublisherOA PDFDOI

• K-MODULI OF CURVES ON A QUADRIC SURFACE AND K3 SURFACES

  Journal of the Institute of Mathematics of Jussieu · 2021 · 15 citations

  Abstract We show that the K-moduli spaces of log Fano pairs $\left(\mathbb {P}^1\times \mathbb {P}^1, cC\right)$ , where C is a $(4,4)$ curve and their wall crossings coincide with the VGIT quotients of $(2,4)$ , complete intersection curves in $\mathbb {P}^3$ . This, together with recent results by Laza and O’Grady, implies that these K-moduli spaces form a natural interpolation between the GIT moduli space of $(4,4)$ curves on $\mathbb {P}^1\times \mathbb {P}^1$ and the Baily–Borel compactific…

  PublisherDOI

• K-moduli of curves on a quadric surface and K3 surfaces

  arXiv (Cornell University) · 2020-06-11 · 5 citations

  preprintOpen access

  We show that the K-moduli spaces of log Fano pairs $(\mathbb{P}^1\times\mathbb{P}^1, cC)$ where $C$ is a $(4,4)$-curve and their wall crossings coincide with the VGIT quotients of $(2,4)$ complete intersection curves in $\mathbb{P}^3$. This, together with recent results by Laza-O'Grady, implies that these K-moduli spaces form a natural interpolation between the GIT moduli space of $(4,4)$-curves on $\mathbb{P}^1\times\mathbb{P}^1$ and the Baily-Borel compactification of moduli of quartic hyperel…

  PublisherOA PDFDOI

• Moduli of boundary polarized Calabi-Yau pairs

  arXiv (Cornell University) · 2023-07-13 · 3 citations

  preprintOpen access

  We develop the moduli theory of boundary polarized CY pairs, which are slc Calabi-Yau pairs $(X,D)$ such that $D$ is ample. The motivation for studying this moduli problem is to construct a moduli space at the Calabi-Yau wall interpolating between certain K-moduli and KSBA moduli spaces. We prove that the moduli stack of boundary polarized CY pairs is S-complete, $Θ$-reductive, and satisfies the existence part of the valuative criterion for properness, which are steps towards constructing a prop…

  PublisherOA PDFDOI

• Moduli of surfaces in $\mathbb{P}^3$

  arXiv (Cornell University) · 2019-03-21 · 3 citations

  preprintOpen access1st authorCorresponding

  The goal of this paper is to construct a compactification of the moduli space of degree $d \ge 5$ surfaces in $\mathbb{P}^3$, i.e. a parameter space whose interior points correspond to (equivalence classes of) smooth surfaces in $\mathbb{P}^3$ and whose boundary points correspond to degenerations of such surfaces. We study a more general problem and consider a divisor $D$ on a Fano variety $Z$ as a pair $(Z, D)$ satisfying certain properties. We find a modular compactification of such pairs and,…

  PublisherOA PDFDOI

Frequent coauthors

• Kenneth Ascher

  University of California, Irvine

  9 shared

• Yuchen Liu

  7 shared

• David C. Stapleton

  3 shared

• David Stapleton

  2 shared

• Amos Turchet

  2 shared

• Xiaowei Wang

  Rutgers, The State University of New Jersey

  1 shared

• Patrick Kennedy-Hunt

  1 shared

• Nikita Singh

  Jacobi Medical Center

  1 shared

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