### Abstract

Given a variation of Hodge structure over P^{1} with Hodge numbers (1, 1,…, 1), we show how to compute the degrees of the Deligne extension of its Hodge bundles, following Eskin–Kontsevich–Möller–Zorich, by using the local exponents of the corresponding Picard– Fuchs equation. This allows us to compute the Hodge numbers of Zucker’s Hodge structure on the corresponding parabolic cohomology groups. We also apply this to families of elliptic curves, K3 surfaces and Calabi–Yau threefolds.

Original language | English (US) |
---|---|

Article number | 045 |

Journal | Symmetry, Integrability and Geometry: Methods and Applications (SIGMA) |

Volume | 13 |

DOIs | |

State | Published - Jun 18 2017 |

### Fingerprint

### Keywords

- Calabi
- Variation of hodge structures
- Yau manifolds

### ASJC Scopus subject areas

- Analysis
- Mathematical Physics
- Geometry and Topology

### Cite this

*Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)*,

*13*, [045]. https://doi.org/10.3842/SIGMA.2017.045

**Hodge numbers from picard–fuchs equations.** / Doran, Charles F.; Harder, Andrew; Thompson, Alan.

Research output: Contribution to journal › Article

*Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)*, vol. 13, 045. https://doi.org/10.3842/SIGMA.2017.045

}

TY - JOUR

T1 - Hodge numbers from picard–fuchs equations

AU - Doran, Charles F.

AU - Harder, Andrew

AU - Thompson, Alan

PY - 2017/6/18

Y1 - 2017/6/18

N2 - Given a variation of Hodge structure over P1 with Hodge numbers (1, 1,…, 1), we show how to compute the degrees of the Deligne extension of its Hodge bundles, following Eskin–Kontsevich–Möller–Zorich, by using the local exponents of the corresponding Picard– Fuchs equation. This allows us to compute the Hodge numbers of Zucker’s Hodge structure on the corresponding parabolic cohomology groups. We also apply this to families of elliptic curves, K3 surfaces and Calabi–Yau threefolds.

AB - Given a variation of Hodge structure over P1 with Hodge numbers (1, 1,…, 1), we show how to compute the degrees of the Deligne extension of its Hodge bundles, following Eskin–Kontsevich–Möller–Zorich, by using the local exponents of the corresponding Picard– Fuchs equation. This allows us to compute the Hodge numbers of Zucker’s Hodge structure on the corresponding parabolic cohomology groups. We also apply this to families of elliptic curves, K3 surfaces and Calabi–Yau threefolds.

KW - Calabi

KW - Variation of hodge structures

KW - Yau manifolds

UR - http://www.scopus.com/inward/record.url?scp=85021180511&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85021180511&partnerID=8YFLogxK

U2 - 10.3842/SIGMA.2017.045

DO - 10.3842/SIGMA.2017.045

M3 - Article

AN - SCOPUS:85021180511

VL - 13

JO - Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)

JF - Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)

SN - 1815-0659

M1 - 045

ER -