2025

• Junyan Cao, Ya Deng, Christopher D. Hacon, Mihai Paun – Hodge theory for local systems and cohomological support loci – arXiv:2511.06773
• Cinzia Bisi, Paolo Cascini, Luca Tasin – Forms and Complex Manifolds – arXiv:2511.06484
• Rahul Ajit – On a Grauert-Riemenschneider vanishing theorem in dimension 3 – arXiv:2511.04906
• Rahul Ajit – Multiplier Modules of extended Rees algebras – arXiv:2510.22074
• Zhiyuan Chen – Finite generation of higher rank quasi-monomial valuations via the extended Rees algebra – arXiv:2510.10737
• Harold Blum, Yuchen Liu, Chenyang Xu, Ziquan Zhuang – Relative stability theory and properness of K-moduli spaces – arXiv:2510.06197
• Paolo Cascini, Jihao Liu, Fanjun Meng, Roberto Svaldi, Lingyao Xie – Variation of algebraically integrable adjoint foliated structures – arXiv:2510.02498
• Junyao Peng – Asymptotics of stability thresholds – arXiv:2509.16458
• Paolo Cascini, Calum Spicer – On base point freeness for rank one foliations – arXiv:2509.03109
• Jingjun Han, Jihao Liu, Ziquan Zhuang – Effective termination of general type MMPs in dimension at most five – arXiv:2509.01501
• János Kollár, Sándor J. Kovács – Higher direct images of dualizing sheaves III – arXiv:2508.16507
• Ivan Cheltsov, Yuri Tschinkel, Zhijia Zhang – Conjugacy classes of linear actions in the plane Cremona group – arXiv:2508.09929
• János Kollár, Giulia Saccà – Sections of Jacobian fibrations over lines – arXiv:2508.09819
• Nicolás Vilches – Stability conditions on surfaces and contractions of curves – arXiv:2508.07019
• János Kollár – A converse of Cartan’s Theorem B for Real Analytic Set – arXiv:2507.11679
• Ivan Cheltsov, DongSeon Hwang, Alex Küronya, Antonio Laface, Frédéric Mangolte, Alex Massarenti, Jihun Park, Junyan Zhao – On K-stability of Fano’s last Fanos – arXiv:2507.08528
• Sándor Kovács, Pat Lank, Sridhar Venkatesh – Simple criteria for higher rational singularities – arXiv:2507.07351
• Hyunsuk Kim – Trace for the Du Bois complex – arXiv:2507.07350
• Jingjun Han, Lu Qi, Ziquan Zhuang – Boundedness in general type MMP – arXiv:2506.20183
• Louis Esser, Jennifer Li – Weighted surfaces with maximal Picard number – arXiv:2506.14037
• Hyunsuk Kim, Sridhar Venkatesh – Lefschetz morphisms on singular cohomology and local cohomological dimension of toric varieties – arXiv:2506.03026
• János Kollár – Birational equivalence of Severi-Brauer varieties – arXiv:2505.24720
• Hamid Abban, Ivan Cheltsov, Takashi Kishimoto, Frederic Mangolte – Smooth Fano 3-folds satisfying Condition (A) – arXiv:2505.13684
• Hyunsuk Kim, Sridhar Venkatesh – Local cohomology and singular cohomology of toric varieties via mixed Hodge modules – arXiv:2505.10417
• Hamid Abban, Ivan Cheltsov, Takashi Kishimoto, Frederic Mangolte – K-stability of Fano 3-folds in the World of Null-A – arXiv:2505.04330
• Christopher Hacon, Joaquín Moraga, José Ignacio Yanez – Bott-Chern complexity of Kähler pairs – arXiv:2505.04303
• Ivan Cheltsov, Lisa Marquand, Yuri Tschinkel, Zhijia Zhang – Equivariant geometry of cubic threefolds with non-isolated singularities – arXiv:2505.03986
• János Kollár – Abelian fiber spaces and their Tate-Shafarevich twists with sections – arXiv:2504.21705
• Joshua Enwright, Jennifer Li, José Ignacio Yáñez – Complexity one varieties are cluster type – arXiv:2504.17369
• Lingyao Xie – The extension of numerically trivial divisors on a family – arXiv:2504.14141
• Paolo Cascini, Jingjun Han, Jihao Liu, Fanjun Meng, Calum Spicer, Roberto Svaldi, Lingyao Xie – On finite generation and boundedness of adjoint foliated structures – arXiv:2504.10737
• Christopher Hacon, Xiaowei Jiang – Failure of Boundedness for Generalised Log Canonical Surfaces – arXiv:2504.06482
• Junyao Peng – $\mathbb{G}_m$-Equivariant Degenerations of del Pezzo Surfaces – arXiv:2503.06612
• Yi-Heng Tsai – Volumes in Calabi-Yau Complete Intersection of Products of Projective Space – arXiv:2503.03949
• Doyoung Choi, Justin Lacini, Jinhyung Park, John Sheridan, Singularities and syzygies of secant varieties of smooth projective varieties – arXiv:2502.19703
• Ivan Cheltsov, Yuri Tschinkel, Zhijia Zhang – Equivariant unirationality of Fano threefolds – arXiv:2502.19598
• Yu-Ting Huang – On the Existence of Good Minimal Models for Kähler Varieties with Projective Albanese Map – arXiv:2502.18800
• János Kollár – Néron models, minimal models, and birational group actions – arXiv:2502.13800
• Qianyu Chen, Mircea Mustata – A birational description of the minimal exponent – arXiv:2502.07233
• Paolo Cascini, Fabrizio Catanese, Yifan Chen, Jong Hae Keum – Mori dream spaces and Q-homology quadrics – arXiv:2501.15589
• Guodu Chen, Jingjun Han, Yang He, Lingyao Xie – Boundedness of complements for generalized pairs – arXiv:2501.03739
• Pat Lank, Peter McDonald, Sridhar Venkatesh – Derived characterizations for rational pairs à la Schwede-Takagi and Kollár-Kovács – arXiv:2501.02783
• Christopher Hacon – Higher dimensional birational geometry and the work of James McKernan – Preprint 2025
• Christopher Hacon – Singularities of the MMP – To appear in Volume VIII of the Handbook of Geometry and Topology of Singularities

2024

• Ivan Cheltsov, Maksym Fedorchuk, Kento Fujita, Anne-Sophie Kaloghiros – K-moduli of pure states of four qubits – arXiv:2412.19972
• Hyunsuk Kim – Canonical bundle formula and a conjecture on certain algebraic fiber spaces by Schnell – arXiv:2412.19769
• János Kollár, Jennifer Li – The Mordell-Schinzel conjecture for cubic diophantine equations – arXiv:2412.12080
• Daniel Bath, Mircea Mustata, Uli Walther – Singularities of square-free polynomials – arXiv:2412.11309
• Christopher Hacon, Omprokash Das – Transcendental Minimal Model Program for Projective Varieties – arXiv:2412.07650
• Ivan Cheltsov, Yuri Tschinkel, Zhijia Zhang – Rationality of singular cubic threefolds over $\mathbb R$ – arXiv:2411.14379
• Giulia Saccà – Compactifying Lagrangian fibrations – arXiv:2411.06505
• Hamid Abban, Ivan Cheltsov, Takashi Kishimoto, Frederic Mangolte – K-stability of pointless del Pezzo surfaces and Fano 3-folds – arXiv:2411.00767
• Qianyu Chen, Bradley Dirks, Sebastian Olano – Restrictions of mixed Hodge modules using generalized V-filtrations – arXiv:2410.09959
• Yuchen Liu, Zhiyu Liu, Chenyang Xu – Irreducible symplectic varieties with a large second Betti number – arXiv:2410.01566 – J. Reine Angew. Math. 825 (2025), 1-31.
• János Kollár – Log K3 surfaces with irreducible boundary – arXiv:2407.08051
• Raisa Serova – Quotients of Jacobians – arXiv:2407.00860
• Zhiyuan Chen – Stable degeneration of families of klt singularities with constant local volume – arXiv:2405.19273 – Form Math. Sigma. 13 (2025), Paper No. e158
• Chenyang Xu, Ziquan Zhuang – Boundedness of log Fano cone singularities and discreteness of local volumes – arXiv:2404.17134
• Ivan Cheltsov, Lisa Marquand, Yuri Tschinkel, Zhijia Zhang – Equivariant geometry of singular cubic threefolds, II – arXiv:2405.02744 – Journal of the London Mathematical Society, Volume 112, Issue 1 (2025), e70224
• Ivan Cheltsov, Oliver Li, Sione Ma’u, Antoine Pinardin – K-stability and space sextic curves of genus three – arXiv:2404.07803