Article
Mathematics
Ling Long, Fang-Ting Tu, Noriko Yui, Wadim Zudilin
Summary: The study establishes supercongruences for rigid hypergeometric Calabi-Yau threefolds using Dwork's theory of p-adic unit roots and the theory of hypergeometric motives. It relies on the modularity of the threefolds and a p-adic perturbation method applied to hypergeometric functions.
ADVANCES IN MATHEMATICS
(2021)
Article
Physics, Mathematical
Thomas W. Grimm, Fabian Ruehle, Damian van de Heisteeg
Summary: A novel way to classify Calabi-Yau threefolds is presented by studying their infinite volume limits, which can be classified by associated limiting mixed Hodge structures. These structures are labeled by a finite number of degeneration types that combine into characteristic degeneration patterns associated to the underlying Calabi-Yau threefold. These patterns provide crucial information encoded in the intersection numbers of Calabi-Yau threefolds.
COMMUNICATIONS IN MATHEMATICAL PHYSICS
(2021)
Article
Mathematics, Applied
Anthony Ashmore
Summary: We present a numerical algorithm for computing the spectrum of the Laplace-de Rham operator on Calabi-Yau manifolds and provide a check of our algorithm by computing the spectrum of eigenforms on P3.
JOURNAL OF GEOMETRY AND PHYSICS
(2024)
Article
Mathematics, Applied
Callum Brodie, Andrei Constantin, Andre Lukas, Fabian Ruehle
Summary: In this paper, we study the flops of Calabi-Yau threefolds realized as Kahler-favourable complete intersections in products of projective spaces (CICYs) and identify two different types. The existence and type of the flops can be recognized from the configuration matrix of the CICY, and examples can be constructed based on this matrix.
JOURNAL OF GEOMETRY AND PHYSICS
(2023)
Article
Mathematics
Nam-Hoon Lee
Summary: The article discusses the concept of non-Gorenstein involutions on Calabi-Yau threefolds, which is a higher dimensional extension of non-symplectic involutions on K3 surfaces. It presents elementary facts about Calabi-Yau threefolds with non-Gorenstein involutions and provides a classification of the Calabi-Yau threefolds of Picard rank one with non-Gorenstein involutions, where the fixed locus is not zero-dimensional.
MATHEMATISCHE NACHRICHTEN
(2023)
Article
Mathematics
Tasuki Kinjo, Naruki Masuda
Summary: In this paper, the authors investigate Keller's deformed Calabi-Yau completion of the derived category of coherent sheaves on a smooth variety. They describe the derived category of the total space of an ?Y-torsor as a certain deformed (n + 1)-Calabi-Yau completion of the derived category of Y. As an application, they investigate the geometry of the derived moduli stack of compactly supported coherent sheaves on a local curve, finding that it is equivalent to the derived critical locus of a function on a certain smooth moduli space. This result is important for the authors' joint work on Higgs bundles and Gopakumar-Vafa invariants.
INTERNATIONAL MATHEMATICS RESEARCH NOTICES
(2023)
Article
Mathematics
P. M. H. Wilson
Summary: This paper investigates boundedness questions for smooth Calabi-Yau threefolds, exploring the possibility of determining them up to finitely many families based on cubic and linear forms. The study focuses on rigid non-movable surfaces and the Picard number 2 case, demonstrating a general boundedness result without special structure assumptions.
JOURNAL OF ALGEBRAIC GEOMETRY
(2021)
Article
Physics, Mathematical
David Erkinger, Johanna Knapp
Summary: This article proposes a universal expression for computing the sphere partition function of Calabi-Yau GLSMs in hybrid phases, which are fibrations of Landau-Ginzburg orbifolds.
COMMUNICATIONS IN MATHEMATICAL PHYSICS
(2022)
Article
Mathematics
Mao Sheng, Jinxing Xu
Summary: We establish a global Torelli theorem for the complete family of Calabi-Yau threefolds arising from cyclic triple covers of P-3 branched along six stable hyperplanes.
COMMUNICATIONS IN MATHEMATICS AND STATISTICS
(2022)
Article
Mathematics
Sheng Meng
Summary: In this paper, we establish a general guideline based on the equivariant minimal model program and the canonical bundle formula, and prove that for a smooth projective threefold X, there exists a polarized endomorphism that makes X of Calabi-Yau type.
INTERNATIONAL MATHEMATICS RESEARCH NOTICES
(2022)
Article
Physics, Particles & Fields
Callum R. Brodie, Andrei Constantin, Andre Lukas, Fabian Ruehle
Summary: This article presents a detailed study of the effective cones of Calabi-Yau threefolds with h(1,1) = 2. It includes the possible types of walls bounding the Kahler cone and a classification of the intersection forms arising in the geometrical phases. The geodesic equation is explicitly solved for all three normal forms in the classification, and is used to analyze the evolution near Kahler cone walls and across flop transitions in the context of M-theory compactifications. Examples from the CICY and Kreuzer-Skarke lists are used to illustrate the structure of the extended Kahler and effective cones, providing a rich set of examples for studying topology change in string theory.
JOURNAL OF HIGH ENERGY PHYSICS
(2022)
Article
Physics, Particles & Fields
Hal Schenck, Mike Stillman, Beihui Yuan
Summary: This article focuses on the ideal IX of projectively normal Calabi-Yau threefolds X, which is arithmetically Gorenstein and has a regularity of four. The case where IX is a complete intersection and the case where X is codimension three have been extensively studied. In the latter case, the Buchsbaum-Eisenbud theorem shows that I-X can be represented by the Pfaffians of a skew-symmetric matrix. Recent papers have investigated the situation when I-X has codimension four. The study proves that there are 16 possible betti tables for an arithmetically Gorenstein ideal I with codimension four and regularity four, and that exactly 8 of these occur for smooth irreducible nondegenerate threefolds. The research also explores higher codimension cases and provides examples of X with h(p,q)(X) that do not appear in lower codimension or as complete intersections in toric Fano varieties. The use of inverse systems is a key tool in this work for identifying potential betti tables for X.
ADVANCES IN THEORETICAL AND MATHEMATICAL PHYSICS
(2022)
Article
Physics, Mathematical
Sibasish Banerjee, Pietro Longhi, Mauricio Romo
Summary: In this study, the BPS spectra of D-branes on local Calabi-Yau threefolds were explored using nonabelianization for exponential networks to calculate unframed BPS indices. By computing new types of BPS invariants of 3d-5d BPS states, known results on these BPS spectra were accurately reproduced through wall-crossing. Additionally, the notion of exponential BPS graphs was developed for the simplest toric examples, showing their encoding of quiver and potential associated to the Calabi-Yau through geometric engineering.
COMMUNICATIONS IN MATHEMATICAL PHYSICS
(2021)
Article
Physics, Particles & Fields
Ross Altman, Jonathan Carifio, Xin Gao, Brent D. Nelson
Summary: We establish an orientifold Calabi-Yau threefold database for h(1,1)(X) <= 6 by considering non-trivial Z(2) divisor exchange involutions, and determine the characteristics and properties of these orientifold Calabi-Yau threefolds.
JOURNAL OF HIGH ENERGY PHYSICS
(2022)
Article
Physics, Particles & Fields
Ambreen Ahmed, M. Nouman Muteeb
Summary: In this article, we investigate the degenerations of mirror curves associated with Calabi-Yau threefolds X-N, X-M, and their effects on the refined topological string partition function. We demonstrate that when the mirror curve degenerates into a union of lower genus curves, the corresponding partition function factorizes into components corresponding to the degenerate mirror curve. Furthermore, we show that by using the degeneration of a generalized mirror curve, it is possible to obtain the partition function corresponding to X-N, X-M-1 from X-N, X-M.
EUROPEAN PHYSICAL JOURNAL C
(2022)
