On the Euler characteristic of a relative hypersurface

Publikation: Bidrag til tidsskrift › Tidsskriftartikel › Forskning › fagfællebedømt

Standard

On the Euler characteristic of a relative hypersurface. / Fullwood, James; Helmer, Martin.

I: Journal of Mathematical Physics, Bind 60, Nr. 5, 052302, 2019.

Publikation: Bidrag til tidsskrift › Tidsskriftartikel › Forskning › fagfællebedømt

Harvard

Fullwood, J & Helmer, M 2019, 'On the Euler characteristic of a relative hypersurface', Journal of Mathematical Physics, bind 60, nr. 5, 052302. https://doi.org/10.1063/1.5030475

APA

Fullwood, J., & Helmer, M. (2019). On the Euler characteristic of a relative hypersurface. Journal of Mathematical Physics, 60(5), [052302]. https://doi.org/10.1063/1.5030475

Vancouver

Fullwood J, Helmer M. On the Euler characteristic of a relative hypersurface. Journal of Mathematical Physics. 2019;60(5). 052302. https://doi.org/10.1063/1.5030475

Author

Fullwood, James ; Helmer, Martin. / On the Euler characteristic of a relative hypersurface. I: Journal of Mathematical Physics. 2019 ; Bind 60, Nr. 5.

Bibtex

@article{d3c34a524f8648b38e1b4d5a1df9030f,
title = "On the Euler characteristic of a relative hypersurface",
abstract = "We derive a general formula for the Euler characteristic of a fibration of projective hypersurfaces in terms of invariants of an arbitrary base variety. When the general fiber is an elliptic curve, such formulas have appeared in the physics literature in the context of calculating D-brane charge for M-/F-theory and type-IIB compactifications of string vacua. While there are various methods for computing Euler characteristics of algebraic varieties, we prove a base-independent pushforward formula which reduces the computation of the Euler characteristic of relative hypersurfaces to simple algebraic manipulations of rational expressions determined by its divisor class in a projective bundle. We illustrate our methods by applying them to an explicit family of relative hypersurfaces whose fibers are of arbitrary dimension and degree.",
author = "James Fullwood and Martin Helmer",
year = "2019",
doi = "10.1063/1.5030475",
language = "English",
volume = "60",
journal = "Journal of Mathematical Physics",
issn = "0022-2488",
publisher = "A I P Publishing LLC",
number = "5",

}

RIS

TY - JOUR

T1 - On the Euler characteristic of a relative hypersurface

AU - Fullwood, James

AU - Helmer, Martin

PY - 2019

Y1 - 2019

N2 - We derive a general formula for the Euler characteristic of a fibration of projective hypersurfaces in terms of invariants of an arbitrary base variety. When the general fiber is an elliptic curve, such formulas have appeared in the physics literature in the context of calculating D-brane charge for M-/F-theory and type-IIB compactifications of string vacua. While there are various methods for computing Euler characteristics of algebraic varieties, we prove a base-independent pushforward formula which reduces the computation of the Euler characteristic of relative hypersurfaces to simple algebraic manipulations of rational expressions determined by its divisor class in a projective bundle. We illustrate our methods by applying them to an explicit family of relative hypersurfaces whose fibers are of arbitrary dimension and degree.

AB - We derive a general formula for the Euler characteristic of a fibration of projective hypersurfaces in terms of invariants of an arbitrary base variety. When the general fiber is an elliptic curve, such formulas have appeared in the physics literature in the context of calculating D-brane charge for M-/F-theory and type-IIB compactifications of string vacua. While there are various methods for computing Euler characteristics of algebraic varieties, we prove a base-independent pushforward formula which reduces the computation of the Euler characteristic of relative hypersurfaces to simple algebraic manipulations of rational expressions determined by its divisor class in a projective bundle. We illustrate our methods by applying them to an explicit family of relative hypersurfaces whose fibers are of arbitrary dimension and degree.

UR - http://www.scopus.com/inward/record.url?scp=85065797800&partnerID=8YFLogxK

U2 - 10.1063/1.5030475

DO - 10.1063/1.5030475

M3 - Journal article

AN - SCOPUS:85065797800

VL - 60

JO - Journal of Mathematical Physics

JF - Journal of Mathematical Physics

SN - 0022-2488

IS - 5

M1 - 052302

ER -

ID: 222754132