Journal ArticleForum of Mathematics Sigma · February 7, 2025
We study the relation between the coregularity, the index of log Calabi-Yau pairs and the complements of Fano varieties. We show that the index of a log Calabi-Yau pair of coregularity is at most, where is the Weil index of. This extends a recent result du ...
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Journal ArticleAlgebra and Number Theory · January 1, 2025
We study the index of log Calabi–Yau pairs (X, B) of coregularity 0. We show that 2λ(KX + B) ∼ 0, where λ is the Weil index of (X, B). This is in contrast to the case of klt Calabi–Yau varieties, where the index can grow doubly exponentially wit ...
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Journal ArticleProceedings of the London Mathematical Society · January 1, 2025
We prove that a geometrically integral smooth projective 3-fold (Formula presented.) with nef anti-canonical class and negative Kodaira dimension over a finite field (Formula presented.) of characteristic (Formula presented.) and cardinality (Formula prese ...
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Journal ArticleJournal of the European Mathematical Society · January 1, 2025
We show that elliptic Calabi–Yau threefolds form a bounded family. We also show that the same result holds for minimal terminal threefolds of Kodaira dimension 2, upon fixing the rate of growth of pluricanonical forms and the degree of a multisection of th ...
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Journal ArticleMichigan Mathematical Journal · September 1, 2024
A conjecture, known as the Shokurov–Kollár connectedness principle, predicts the following. Let (X, B) be a pair, and let f : X → S be a contraction with −(KX + B) nef over S; then, for any point s ∈ S, the intersection f −1 (s) ∩ Nkl ...
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Journal ArticleAlgebraic Geometry · January 1, 2024
In this note, we study certain sufficient conditions for a set of minimal klt pairs (X, Δ) with κ(X, Δ) = dim(X) − 1 to be bounded. ...
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Journal ArticleBulletin of the London Mathematical Society · January 1, 2024
We show that mixed-characteristic and equi-characteristic small deformations of 3-dimensional canonical (resp., terminal) singularities with perfect residue field of characteristic (Formula presented.) are canonical (resp., terminal). We discuss applicatio ...
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Journal ArticleJournal of Algebraic Geometry · January 1, 2024
We develop a framework to construct moduli spaces of Q-Gorenstein pairs. To do so, we fix certain invariants; these choices are encoded in the notion of Q-stable pair. We show that these choices give a proper moduli space with projective coarse moduli spac ...
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Journal ArticleForum of Mathematics Sigma · April 24, 2023
Let be a pair, and let be a contraction with nef over S. A conjecture, known as the Shokurov-Kollár connectedness principle, predicts that has at most two connected components, where is an arbitrary schematic point and denotes the non-klt locus of. In this ...
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Journal ArticleGeometry and Topology · January 1, 2022
We show the Jordan property for regional fundamental groups of klt singularities of fixed dimension. Furthermore, we prove the existence of effective simultaneous index 1 covers for n–dimensional klt singularities. We give an application to the study of lo ...
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Journal ArticleProceedings of the Edinburgh Mathematical Society · May 1, 2020
In this note, using methods introduced by Hacon et al. ['Boundedness of varieties of log general type', Proceedings of Symposia in Pure Mathematics, Volume 97 (American Mathematical Society, Providence, RI, 2018) 309-348], we study the accumulation points ...
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Journal ArticleAnnali Della Scuola Normale Superiore Di Pisa Classe Di Scienze · January 1, 2020
In this note, we extend the theories of the canonical bundle formula and adjunction to the case of generalized pairs. As an application, we study a particular case of a conjecture by Prokhorov and Shokurov. ...
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Journal ArticleDocumenta Mathematica · January 1, 2020
We prove the boundedness of global strong (δ, n)- complements for generalized ∈-log canonical pairs of Fano-type. We also prove some partial results towards boundedness of local strong (δ, n)-complements for semi-stable morphisms. As applications, we prove ...
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Journal ArticleTaiwanese Journal of Mathematics · August 1, 2018
In this paper, we study the behavior of the sets of volumes of the form vol(X;KX + B +M), where (X;B) is a log canonical pair, and M is a nef ℝ-divisor. After a first analysis of some general properties, we focus on the case when M is ℚ-Cartier with given ...
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Journal ArticleBolletino Dell Unione Matematica Italiana · June 1, 2018
We show that there exist smooth surfaces violating Generic Vanishing in any characteristic p≥ 3. As a corollary, we recover a result of Hacon and Kovács, producing counterexamples to Generic Vanishing in dimension 3 and higher. ...
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Journal ArticleMatematiche · January 1, 2018
We study an example of complete intersection Calabi-Yau threefold due to Libgober and Teitelbaum [11], and verify mirror symmetry at a cohomological level. Direct computations allow us to propose an analogue to the Berglund-Hübsch mirror symmetry setup for ...
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