On (2, 4) complete intersection threefolds that contain an Enriques surface

Lev A. Borisov; Howard J. Nuer

doi:10.1007/s00209-016-1676-z

On (2, 4) complete intersection threefolds that contain an Enriques surface

Research output: Contribution to journal › Article › peer-review

Abstract

We study nodal complete intersection threefolds of type (2, 4) in P⁵ which contain an Enriques surface in its Fano embedding. We completely determine Calabi–Yau birational models of a generic such threefold. These models have Hodge numbers h¹¹= 2 , h¹²= 32. We also describe Calabi–Yau varieties with Hodge numbers (h¹¹, h¹²) equal to (2, 26), (23, 5) and (31, 1). The last two pairs of Hodge numbers are, to the best of our knowledge, new.

Original language	English
Pages (from-to)	853-876
Number of pages	24
Journal	Mathematische Zeitschrift
Volume	284
Issue number	3-4
DOIs	https://doi.org/10.1007/s00209-016-1676-z
State	Published - 1 Dec 2016
Externally published	Yes

Keywords

Calabi–Yau threefolds
Enriques surfaces
Minimal model program

ASJC Scopus subject areas

General Mathematics

Access to Document

10.1007/s00209-016-1676-z

Cite this

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title = "On (2, 4) complete intersection threefolds that contain an Enriques surface",

abstract = "We study nodal complete intersection threefolds of type (2, 4) in P5 which contain an Enriques surface in its Fano embedding. We completely determine Calabi–Yau birational models of a generic such threefold. These models have Hodge numbers h11= 2 , h12= 32. We also describe Calabi–Yau varieties with Hodge numbers (h11, h12) equal to (2, 26), (23, 5) and (31, 1). The last two pairs of Hodge numbers are, to the best of our knowledge, new.",

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AB - We study nodal complete intersection threefolds of type (2, 4) in P5 which contain an Enriques surface in its Fano embedding. We completely determine Calabi–Yau birational models of a generic such threefold. These models have Hodge numbers h11= 2 , h12= 32. We also describe Calabi–Yau varieties with Hodge numbers (h11, h12) equal to (2, 26), (23, 5) and (31, 1). The last two pairs of Hodge numbers are, to the best of our knowledge, new.

KW - Calabi–Yau threefolds

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KW - Minimal model program

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