Periods of singular double octic Calabi–Yau threefolds and modular forms
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DOI: 10.1002/mana.202200085
Abstract: By the modularity theorem every rigid Calabi-Yau threefold $X$ has associated modular form $f$ such that the equality of $L$-functions $L(X,s)=L(f,s)$ holds. In this case period integrals of $X$ are expected to be expressible in… read more here.
Keywords: singular double; calabi; calabi yau; double octic ... See more keywords
Bounding the Kreuzer‐Skarke Landscape
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DOI: 10.1002/prop.202000086
Abstract: We study Calabi-Yau threefolds with large Hodge numbers by constructing and counting triangulations of reflexive polytopes. By counting points in the associated secondary polytopes, we show that the number of fine, regular, star triangulations of… read more here.
Keywords: calabi yau; number; skarke landscape; bounding kreuzer ... See more keywords
Modular amplitudes and flux-superpotentials on elliptic Calabi-Yau fourfolds
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DOI: 10.1007/jhep01(2018)086
Abstract: A bstractWe discuss the period geometry and the topological string amplitudes on elliptically fibered Calabi-Yau fourfolds in toric ambient spaces. In particular, we describe a general procedure to fix integral periods. Using some elementary facts… read more here.
Keywords: calabi yau; modular amplitudes; amplitudes flux; yau fourfolds ... See more keywords
Calabi-Yau manifolds and SU(3) structure
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DOI: 10.1007/jhep01(2019)171
Abstract: A bstractWe show that non-trivial SU(3) structures can be constructed on large classes of Calabi-Yau three-folds. Specifically, we focus on Calabi-Yau three-folds constructed as complete intersections in products of projective spaces, although we expect similar… read more here.
Keywords: yau manifolds; manifolds structure; calabi yau;
Topological strings on singular elliptic Calabi-Yau 3-folds and minimal 6d SCFTs
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DOI: 10.1007/jhep03(2018)156
Abstract: A bstractWe apply the modular approach to computing the topological string partition function on non-compact elliptically fibered Calabi-Yau 3-folds with higher Kodaira singularities in the fiber. The approach consists in making an ansatz for the… read more here.
Keywords: function; calabi yau; yau folds; partition function ... See more keywords
Counting perverse coherent systems on Calabi–Yau 4-folds
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DOI: 10.1007/s00208-022-02364-1
Abstract: Nagao-Nakajima introduced counting invariants of stable perverse coherent systems on small resolutions of Calabi-Yau 3-folds and determined them on the resolved conifold. Their invariants recover DT/PT invariants and Szendroi's non-commutative invariants in some chambers of… read more here.
Keywords: counting invariants; coherent systems; calabi yau; yau folds ... See more keywords
Homogeneous Contact Manifolds and Resolutions of Calabi–Yau Cones
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DOI: 10.1007/s00220-019-03337-3
Abstract: In the present work we provide a constructive method to describe contact structures on compact homogeneous contact manifolds. The main feature of our approach is to describe the Cartan–Ehresmann connection (gauge field) for principal U(1)-bundles… read more here.
Keywords: calabi yau; homogeneous contact; resolutions calabi; yau cones ... See more keywords
Genus zero Gopakumar–Vafa type invariants for Calabi–Yau 4-folds
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DOI: 10.1016/j.aim.2018.08.013
Abstract: Abstract In analogy with the Gopakumar–Vafa conjecture on CY 3-folds, Klemm and Pandharipande defined GV type invariants on Calabi–Yau 4-folds using Gromov–Witten theory and conjectured their integrality. In this paper, we propose a sheaf-theoretic interpretation… read more here.
Keywords: genus zero; calabi yau; yau folds; type invariants ... See more keywords
On syzygies of Calabi–Yau varieties and varieties of general type
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DOI: 10.1016/j.aim.2018.12.002
Abstract: Abstract We establish projective normality, Property N p and effective very ampleness for line bundles on a Calabi–Yau variety, as well as for pluricanonical bundles of a variety of general type. We also prove a… read more here.
Keywords: general type; varieties varieties; calabi yau; yau varieties ... See more keywords
Calabi-Yau algebras and the shifted noncommutative symplectic structure
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DOI: 10.1016/j.aim.2020.107126
Abstract: In this paper we show that for a Koszul Calabi-Yau algebra, there is a shifted bi-symplectic structure in the sense of Crawley-Boevey-Etingof-Ginzburg, on the cobar construction of its co-unitalized Koszul dual coalgebra, and hence its… read more here.
Keywords: calabi yau; yau algebras; symplectic structure; algebras shifted ... See more keywords
Curve counting and DT/PT correspondence for Calabi-Yau 4-folds
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DOI: 10.1016/j.aim.2020.107371
Abstract: Abstract Recently, Cao-Maulik-Toda defined stable pair invariants of a compact Calabi-Yau 4-fold X. Their invariants are conjecturally related to the Gopakumar-Vafa type invariants of X defined using Gromov-Witten theory by Klemm-Pandharipande. In this paper, we… read more here.
Keywords: calabi yau; yau folds; correspondence; yau ... See more keywords