THE GEOMETRY OF BIELLIPTIC SURFACES IN ℙ<sup>4</sup>

Aure, Alf; Decker, Wolfram; Popescu, Sorin; Hulek, Klaus; Ranestad, Kristian

doi:10.1142/s0129167x93000406

Cited by 15 publications

(55 citation statements)

References 10 publications

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“…For (2), note that from (1.3), either a ij = 0 or C 3 = ξ 2i−2j . Thus C 3 must be of the form C 3 = ξ 2m , and then a ij = 0 unless 2(i − j) ≡ 2m mod 2d.…”

Section: ) This Proves (1)mentioning

confidence: 99%

“…(2) The closure of the image of φ, im φ, is a complete intersection of type (2,3) whose equations are the Plücker quadric z 0 z 5 − z 1 z 4 + z 2 z 3 = 0 and the cubic Proof. (1) One easily checks that the zero locus of the six quadrics defining the map φ is P 1 ∪ P 2 .…”

Section: Moduli Of (1 14)-polarized Abelian Surfacesmentioning

confidence: 99%

“…There is one other example of a Calabi-Yau three-fold arising in this paper, a linear section of Gr (2,7), containing a pencil of (1,14) abelian surfaces. In fact it turns out to be birational to the Pfaffian Calabi-Yau of degree 14 in P 6 containing a pencil of (1, 7) abelian surfaces.…”

Section: Introductionmentioning

confidence: 99%

“…. , z 5 as the Plücker quadric, π •φ (Q 2 ) is then the complete intersection of this Plücker quadric and the cubic hypersurface, showing (2).…”

mentioning

confidence: 98%

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Calabi-Yau three-folds and moduli of abelian surfaces II

Gross

Popescu

2011

Trans. Amer. Math. Soc.

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Abstract. We give explicit descriptions of the moduli spaces of abelian surfaces with polarizations of type (1, d), for d = 12, 14, 16, 18 and 20. More precisely, in each case we show that a certain choice of moduli space of such abelian surfaces with a partial level structure can be described explicitly and is unirational, and in some cases rational. These moduli spaces with partial level structure are covers of the ordinary moduli spaces, so the Kodaira dimension of the ordinary moduli spaces in these cases is −∞. In addition, we give a few new examples of Calabi-Yau three-folds fibred in abelian surfaces. In the case of d = 20, such Calabi-Yau three-folds play a key role in the description of the abelian surfaces.

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“…For (2), note that from (1.3), either a ij = 0 or C 3 = ξ 2i−2j . Thus C 3 must be of the form C 3 = ξ 2m , and then a ij = 0 unless 2(i − j) ≡ 2m mod 2d.…”

Section: ) This Proves (1)mentioning

confidence: 99%

Section: Moduli Of (1 14)-polarized Abelian Surfacesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

“…. , z 5 as the Plücker quadric, π •φ (Q 2 ) is then the complete intersection of this Plücker quadric and the cubic hypersurface, showing (2).…”

mentioning

confidence: 98%

See 2 more Smart Citations

Calabi-Yau three-folds and moduli of abelian surfaces II

Gross

Popescu

2011

Trans. Amer. Math. Soc.

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show abstract

“…1 Not to be confused with another Hesse's configuration (12 4 , 16 3 ), also related to plane cubic curves, see [15]. 2 The term "syzygy" originates in astronomy where three planets are in syzygy when they are in line. Sylvester used this word to express a linear relation between a form and its covariant.…”

Section: Introductionmentioning

confidence: 99%