Surfaces on quintic threefolds associated to the Horrocks-Mumford bundle

Aure, Alf

doi:10.1007/bfb0095964

Cited by 10 publications

(28 citation statements)

References 6 publications

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“…By [15], Corollary 2.7, if A ⊆ P 11 is an H 12 -invariant abelian surface with polarization of type (1,12), with y ∈ A a point, then M 6 (x, y) has rank at most two on A. So in particular, if x ∈ A ∩ P 4 − , the matrix M 6 (x, x) must have rank at most two.…”

Section: Moduli Of (1 12)-polarized Abelian Surfacesmentioning

confidence: 99%

“…Following the strategy for (1,12), one finds that the matrix M 7 (x, x) has rank 2 on a quartic hypersurface f 1 = 0 in P 5 − , and the matrix M 7 (σ(x), x) has rank 2 on another quartic hypersurface f 2 = 0. One finds f 1 = f 2 = 0 is an irreducible three-fold, and hence is the closure of the locus of odd 2-torsion points, Z 14 in the notation of [15], §6.…”

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

confidence: 99%

“…Our goal now is to understand A H 16 with H = 2K (1,16). In this case, GL H is a four-dimensional group, as computed in Proposition 1.4.…”

Section: Moduli Of (1 16)-polarized Abelian Surfacesmentioning

confidence: 99%

“…Here we use the fact that there exist singular quintics in P 4 which contain pencils of (non-minimal) (1,20)-polarized abelian surfaces. This yields a ruling of A H 20 .…”

Section: Introductionmentioning

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%

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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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Section: Moduli Of (1 12)-polarized Abelian Surfacesmentioning

confidence: 99%

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

confidence: 99%

“…Our goal now is to understand A H 16 with H = 2K (1,16). In this case, GL H is a four-dimensional group, as computed in Proposition 1.4.…”

Section: Moduli Of (1 16)-polarized Abelian Surfacesmentioning

confidence: 99%

“…Here we use the fact that there exist singular quintics in P 4 which contain pencils of (non-minimal) (1,20)-polarized abelian surfaces. This yields a ruling of A H 20 .…”

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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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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Irregular elliptic surfaces of degree 12 in projective fourspace

Abo

Ranestad

2005

Mathematische Nachrichten

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So far a few families of smooth irregular surfaces are known to exist in P 4 up to pullbacks by suitable finite morphisms from P 4 onto P 4 itself. In this paper we present two different constructions of irregular smooth minimal elliptic surfaces of degree 12 in P 4 . The first is a monad construction while the other uses liaison. The family constructed via liaison includes the surfaces of the first family as a special case.

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