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The KSBA moduli space of stable log Calabi-Yau surfaces
Multi angle
Authors : Argüz, Hülya (Author of the conference)
CIRM (Publisher )
14D20 - Algebraic moduli problems, moduli of vector bundles
14E30 - Minimal model program (Mori theory, extremal rays)
14Q10 - Surfaces, hypersurfaces
CIRM (Publisher )
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Abstract :
The KSBA moduli space of stable pairs ($\mathrm{X}, \mathrm{B}$), introduced by Kollár-Shepherd-Barron, and Alexeev, is a natural generalization of the moduli space of stable curves for higher dimensional varieties. This moduli space is described concretely only in a handful of situations. For instance, if $\mathrm{X}$ is a toric variety and $\mathrm{B}=\mathrm{D}+\varepsilon\mathrm{C}_{}^{}$, where D is the toric boundary divisor and $\mathrm{C}$ is an ample divisor, it is shown by Alexeev that the KSBA moduli space is a toric variety. More generally,for stable pairs of the form$\left( \mathrm{{X,D}+\varepsilon\mathrm{C}} \right)$ with $\left( \mathrm{X,D} \right)$ a log Calabi–Yau variety and C an ample divisor, it was conjectured by Hacking–Keel–Yu that the KSBA moduli space is still toric, up to passing to a finite cover. In joint work with Alexeev and Bousseau, we prove this conjecture for all log Calabi-Yau surfaces. This uses tools from the minimal model program, log geometry and mirror symmetry.
Keywords : moduli spaces; log Valabi-Yau surfaces
MSC Codes : Keywords : moduli spaces; log Valabi-Yau surfaces
14D20 - Algebraic moduli problems, moduli of vector bundles
14E30 - Minimal model program (Mori theory, extremal rays)
14Q10 - Surfaces, hypersurfaces
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Information on the Video
Film maker : Recanzone, LucaLanguage : English Available date : 14/02/2025 Conference Date : 28/01/2025 Subseries : Research School arXiv category : Algebraic Geometry Mathematical Area(s) : Algebraic & Complex Geometry Format : MP4 (.mp4) - HD Video Time : 00:54:41 Targeted Audience : Researchers ; Graduate Students ; Doctoral Students, Post-Doctoral Students Download : https://videos.cirm-math.fr/2025-01-28_Arguz.mp4 
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Information on the Event
Event Title : Logarithmic and non-archimedean methods in Singularity Theory - Thematic Month Week 1 / Méthodes logarithmiques et non-archimédiennes en théorie des singularités - Mois thématique semaine 1Event Organizers : Fantini, Lorenzo ; Pełka, Tomasz ; Pichon, Anne ; Rond, Guillaume Dates : 27/01/2025 - 31/01/2025 Event Year : 2025 Event URL : https://conferences.cirm-math.fr/3267.html
Citation Data
DOI : 10.24350/CIRM.V.20292703Cite this video as: Argüz, Hülya (2025). The KSBA moduli space of stable log Calabi-Yau surfaces. CIRM. Audiovisual resource. doi:10.24350/CIRM.V.20292703 URI : http://dx.doi.org/10.24350/CIRM.V.20292703 |
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Bibliography
- ALEXEEV, Valery, ARGÜZ, Hülya, et BOUSSEAU, Pierrick. The KSBA moduli space of stable log Calabi-Yau surfaces. arXiv preprint arXiv:2402.15117, 2024. - https://doi.org/10.48550/arXiv.2402.15117
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