2015
DOI: 10.1007/978-3-319-17987-2_2
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Classifications of Elliptic Fibrations of a Singular K3 Surface

Abstract: We classify, up to automorphisms, the elliptic fibrations on the singular K3 surface X whose transcendental lattice is isometric to 6 ⊕ 2 .

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Cited by 12 publications
(21 citation statements)
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“…Moreover, if π is branched over two different smooth fibers, τ (C) = C implies that τ is an involution of C, and thus D is a section of the elliptic fibration E R . Hence if D is a component of a fiber one must have τ (C) = C, i.e., case (2) with m = 0.…”
Section: Rational Curves On K3 Surfacesmentioning
confidence: 99%
See 2 more Smart Citations
“…Moreover, if π is branched over two different smooth fibers, τ (C) = C implies that τ is an involution of C, and thus D is a section of the elliptic fibration E R . Hence if D is a component of a fiber one must have τ (C) = C, i.e., case (2) with m = 0.…”
Section: Rational Curves On K3 Surfacesmentioning
confidence: 99%
“…Since X is a double cover of an extremal rational elliptic surface R branched on smooth fibers, the reducible fibers of the inherited fibration E X contribute with 16 components to a set of generators of NS(X). If X is generic among such surfaces then it lies in a 2-dimensional family and hence NS(X) has 2 We exclude rational elliptic surfaces with (2I * 0 ). These have a 1-dimensional moduli space.…”
Section: Double Covers Of Extremal Rational Elliptic Surfacesmentioning
confidence: 99%
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“…12 Elliptic fibrations with a global section, and their Weierstrass forms, of an attractive K3 surface whose transcendental lattice has the intersection matrix 4 0 0 2 are classified in [58]. Elliptic fibrations with a global section of an attractive K3 surface whose transcendental lattice has the intersection matrix 6 0 0 2 are studied in [59].…”
Section: Enhancement To Models With U (1)mentioning
confidence: 99%
“…In Section 4, we recall Borcherds method, and apply it to 11 singular K3 surfaces whose transcendental lattices are listed in Table 4.1. Recently, many geometric studies of singular K3 surfaces of small discriminant have appeared (see, for example, [3], [12], [21], [40]). We summarize the computational data for these 11 singular K3 surfaces in Table 4.2.…”
Section: Introductionmentioning
confidence: 99%