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pro vyhledávání: '"Blum, Harold P."'
Autor:
Blum, Harold, Liu, Yuchen
We construct projective asymptotically good moduli spaces parametrizing boundary polarized CY surface pairs, which are projective slc Calabi-Yau pairs $(X,D)$ such that $D$ is ample and $X$ has dimension two. The moduli space provides a wall crossing
Externí odkaz:
http://arxiv.org/abs/2407.00850
Autor:
Ascher, Kenneth, Bejleri, Dori, Blum, Harold, DeVleming, Kristin, Inchiostro, Giovanni, Liu, Yuchen, Wang, Xiaowei
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 ce
Externí odkaz:
http://arxiv.org/abs/2307.06522
We prove that the multiplicity of a filtration of a local ring satisfies various convexity properties. In particular, we show the multiplicity is convex along geodesics. As a consequence, we prove that the volume of a valuation is log convex on simpl
Externí odkaz:
http://arxiv.org/abs/2208.04902
Publikováno v:
Forum Math. Pi 11 (2023), Paper No. e9, 28 pp
We prove an algebraic version of the Hamilton-Tian Conjecture for all log Fano pairs. More precisely, we show that any log Fano pair admits a canonical two-step degeneration to a reduced uniformly Ding stable triple, which admits a K\"ahler-Ricci sol
Externí odkaz:
http://arxiv.org/abs/2103.15278
We establish an algebraic approach to prove the properness of moduli spaces of K-polystable Fano varieties and reduce the problem to a conjecture on destabilizations of K-unstable Fano varieties. Specifically, we prove that if the stability threshold
Externí odkaz:
http://arxiv.org/abs/2011.01895
Akademický článek
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Publikováno v:
Geom. Topol. 26 (2022) 2507-2564
We show that for a K-unstable Fano variety, any divisorial valuation computing its stability threshold induces a non-trivial special test configuration preserving the stability threshold. When such a divisorial valuation exists, we show that the Fano
Externí odkaz:
http://arxiv.org/abs/1907.05399
In this paper, we prove the openness of K-semistability in families of log Fano pairs by showing that the stability threshold is a constructible function on the fibers. We also prove that any special test configuration arises from a log canonical pla
Externí odkaz:
http://arxiv.org/abs/1907.02408
We prove that K-polystable log Fano pairs have reductive automorphism groups. In fact, we deduce this statement by establishing more general results concerning the S-completeness and $\Theta$-reductivity of the moduli of K-semistable log Fano pairs.
Externí odkaz:
http://arxiv.org/abs/1906.03122
Autor:
Blum, Harold, Xu, Chenyang
We prove that K-polystable degenerations of Q-Fano varieties are unique. Furthermore, we show that the moduli stack of K-stable Q-Fano varieties is separated. Together with [Jia17,BL18], the latter result yields a separated Deligne-Mumford stack para
Externí odkaz:
http://arxiv.org/abs/1812.03538