Relevant bibliographies by topics / Picard lattice

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  1. Journal articles
  2. Dissertations / Theses
  3. Book chapters
  4. Conference papers

Academic literature on the topic 'Picard lattice'

Author: Grafiati
Published: 9 March 2023
Last updated: 10 March 2023

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Journal articles on the topic "Picard lattice"

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Várilly-Alvarado, Anthony, and David Zywina. "Arithmetic E8 Lattices with Maximal Galois Action." LMS Journal of Computation and Mathematics 12 (2009): 144–65. http://dx.doi.org/10.1112/s1461157000001479.

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AbstractWe construct explicit examples of E8 lattices occurring in arithmetic for which the natural Galois action is equal to the full group of automorphisms of the lattice, i.e., the Weyl group of E8. In particular, we give explicit elliptic curves over Q(t) whose Mordell-Weil lattices are isomorphic to E8 and have maximal Galois action.Our main objects of study are del Pezzo surfaces of degree 1 over number fields. The geometric Picard group, considered as a lattice via the negative of the intersection pairing, contains a sublattice isomorphic to E8. We construct examples of such surfaces fo
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Sarti, Alessandra. "Group Actions, Cyclic Coverings and Families of K3-Surfaces." Canadian Mathematical Bulletin 49, no. 4 (2006): 592–608. http://dx.doi.org/10.4153/cmb-2006-055-0.

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AbstractIn this paper we describe six pencils of K3-surfaces which have large Picard number (ρ = 19, 20) and each contains precisely five special fibers: four have A-D-E singularities and one is non-reduced. In particular, we characterize these surfaces as cyclic coverings of some K3-surfaces described in a recent paper by Barth and the author. In many cases, using 3-divisible sets, resp., 2-divisible sets, of rational curves and lattice theory, we describe explicitly the Picard lattices.
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Kondō, Shigeyuki. "Algebraic K3 surfaces with finite automorphism groups." Nagoya Mathematical Journal 116 (December 1989): 1–15. http://dx.doi.org/10.1017/s0027763000001653.

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The purpose of this paper is to give a proof to the result announced in [3]. Let X be an algebraic surface defined over C. X is called a K3 surface if its canonical line bundle Kx is trivial and dim H1(X, ϕX) = 0. It is known that the automorphism group Aut (X) of X is isomorphic, up to a finite group, to the factor group O(Sx)/Wx, where O(Sx) is the automorphism group of the Picard lattice of X (i.e. Sx is the Picard group of X together with the intersection form) and Wx is its subgroup generated by all reflections associated with elements with square (–2) of Sx ([11]). Recently Nikulin [8],
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ZHAO, TIEHONG. "A minimal volume arithmetic cusped complex hyperbolic orbifold." Mathematical Proceedings of the Cambridge Philosophical Society 150, no. 2 (2010): 313–42. http://dx.doi.org/10.1017/s0305004110000526.

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AbstractThe sister of Eisenstein–Picard modular group is described explicitly in [10], whose quotient is a noncompact arithmetic complex hyperbolic 2-orbifold of minimal volume (see [16]). We give a construction of a fundamental domain for this group. A presentation of that lattice can be obtained from that construction, which relates to one of Mostow's lattices.
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Eisele, Florian. "On the geometry of lattices and finiteness of Picard groups." Journal für die reine und angewandte Mathematik (Crelles Journal) 2022, no. 782 (2021): 219–33. http://dx.doi.org/10.1515/crelle-2021-0064.

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Abstract Let ( K , 𝒪 , k ) {(K,\mathcal{O},k)} be a p-modular system with k algebraically closed and 𝒪 {\mathcal{O}} unramified, and let Λ be an 𝒪 {\mathcal{O}} -order in a separable K-algebra. We call a Λ-lattice L rigid if Ext Λ 1 ⁡ ( L , L ) = 0 {{\operatorname{Ext}}^{1}_{\Lambda}(L,L)=0} , in analogy with the definition of rigid modules over a finite-dimensional algebra. By partitioning the Λ-lattices of a given dimension into “varieties of lattices”, we show that there are only finitely many rigid Λ-lattices L of any given dimension. As a consequence we show that if the first Hochschild c
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Fisher, Tom. "Explicit moduli spaces for congruences of elliptic curves." Mathematische Zeitschrift 295, no. 3-4 (2019): 1337–54. http://dx.doi.org/10.1007/s00209-019-02392-9.

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Abstract We determine explicit birational models over $${{\mathbb {Q}}}$$ Q for the modular surfaces parametrising pairs of N-congruent elliptic curves in all cases where this surface is an elliptic surface. In each case we also determine the rank of the Mordell–Weil lattice and the geometric Picard number.
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Aprodu, Marian, and Gavril Farkas. "Green’s conjecture for curves on arbitrary K3 surfaces." Compositio Mathematica 147, no. 3 (2011): 839–51. http://dx.doi.org/10.1112/s0010437x10005099.

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AbstractGreen’s conjecture predicts than one can read off special linear series on an algebraic curve, by looking at the syzygies of its canonical embedding. We extend Voisin’s results on syzygies of K3 sections, to the case of K3 surfaces with arbitrary Picard lattice. This, coupled with results of Voisin and Hirschowitz–Ramanan, provides a complete solution to Green’s conjecture for smooth curves on arbitrary K3 surfaces.
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Camere, Chiara, Grzegorz Kapustka, Michał Kapustka, and Giovanni Mongardi. "Verra Four-Folds, Twisted Sheaves, and the Last Involution." International Mathematics Research Notices 2019, no. 21 (2018): 6661–710. http://dx.doi.org/10.1093/imrn/rnx327.

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Abstract We study the geometry of some moduli spaces of twisted sheaves on K3 surfaces. In particular we introduce induced automorphisms from a K3 surface on moduli spaces of twisted sheaves on this K3 surface. As an application we prove the unirationality of moduli spaces of irreducible holomorphic symplectic manifolds of K3[2]-type admitting non-symplectic involutions with invariant lattices U(2) ⊕ D4(−1) or U(2) ⊕ E8(−2). This complements the results obtained in [43], [13], and the results from [29] about the geometry of irreducible holomorphic symplectic (IHS) four-folds constructed using
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CATINAS, TEODORA, DIANA OTROCOL, and IOAN A. RUS. "The iterates of positive linear operators with the set of constant functions as the fixed point set." Carpathian Journal of Mathematics 32, no. 2 (2016): 165–72. http://dx.doi.org/10.37193/cjm.2016.02.04.

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Let Ω ⊂ Rp, p ∈ N∗ be a nonempty subset and B(Ω) be the Banach lattice of all bounded real functions on Ω, equipped with sup norm. Let X ⊂ B(Ω) be a linear sublattice of B(Ω) and A: X → X be a positive linear operator with constant functions as the fixed point set. In this paper, using the weakly Picard operators techniques, we study the iterates of the operator A. Some relevant examples are also given.
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Yakovenko, Sergei. "Bounded decomposition in the Brieskorn lattice and Pfaffian Picard–Fuchs systems for Abelian integrals." Bulletin des Sciences Mathématiques 126, no. 7 (2002): 535–54. http://dx.doi.org/10.1016/s0007-4497(02)01126-0.

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Dissertations / Theses on the topic "Picard lattice"

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Festi, D. "Topics in the arithmetic of Del Pezzo and K3 surfaces." Doctoral thesis, Università degli Studi di Milano, 2016. http://hdl.handle.net/2434/411137.

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In this thesis we study the arithmetic of certain del Pezzo surfaces and K3 surfaces.We prove that all the del Pezzo surfaces of degree 2 over a finite field are unirational. We compute the Picard lattice of the members of a family of K3 surfaces given by double covers of the projective plane. Finally, we provide an explicit example of a K3 surface over the field of rational numbers with a particular Picard lattice of rank 2.
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Book chapters on the topic "Picard lattice"

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"§2. PICARD GROUP AND COHOMOLOGY." In Commensurabilities among Lattices in PU (1,n). (AM-132). Princeton University Press, 1993. http://dx.doi.org/10.1515/9781400882519-003.

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Conference papers on the topic "Picard lattice"

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Liu, Zhenhai, Feipeng Qi, Yi Zhou, et al. "The Study of Coupled Fuel Performance Analysis and Neutronics With COMSOL and RMC." In 2022 29th International Conference on Nuclear Engineering. American Society of Mechanical Engineers, 2022. http://dx.doi.org/10.1115/icone29-92046.

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Abstract Predicting fuel behavior in the reactor is a typical multi-physics coupling problem. The traditional fuel performance analysis adopts a decoupling way. To provide a higher fidelity tool for fuel performance simulation, the multi-physics coupling software COMSOL and 3D Monte Carlo neutron transport code RMC are coupled. The fuel rod thermo-mechanical coupling analysis module is constructed in COMSOL. RMC is innovatively wrapped as a component of COMSOL to communicate with the fuel performance module. Grid mapping algorithm is set up using COMSOL’s functionality. A carefully designed se
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