Classifying weighted projective spaces

Anthony Bahri; Matthias Franz; Dietrich Notbohm; Nigel Ray

Classifying weighted projective spaces

Anthony Bahri
, Matthias Franz
, Dietrich Notbohm
, Nigel Ray

Research output: Preprint/Working paper › Working paper

Abstract

We obtain two classiﬁcations of complex weighted projective spaces, up to homeomorphism and up to homotopy equivalence. The ﬁrst turns out to coincide with Al Amrani’s classiﬁcation up to isomorphism of algebraic varieties, and the second follows from our proof that the Mislin genus of any weighted projective space is rigid.

Original language	English
Place of Publication	arXiv.org
Number of pages	7
Publication status	Published - Sept 2011

Keywords

Classification problem, homeomorphism, homotopy equivalence, weighted projective space

Cite this

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title = "Classifying weighted projective spaces",

abstract = "We obtain two classiﬁcations of complex weighted projective spaces, up to homeomorphism and up to homotopy equivalence. The ﬁrst turns out to coincide with Al Amrani{\textquoteright}s classiﬁcation up to isomorphism of algebraic varieties, and the second follows from our proof that the Mislin genus of any weighted projective space is rigid.",

keywords = "Classification problem, homeomorphism, homotopy equivalence, weighted projective space",

author = "Anthony Bahri and Matthias Franz and Dietrich Notbohm and Nigel Ray",

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year = "2011",

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AU - Franz, Matthias

AU - Notbohm, Dietrich

AU - Ray, Nigel

N1 - This paper has been submitted to an academic journal.

PY - 2011/9

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N2 - We obtain two classiﬁcations of complex weighted projective spaces, up to homeomorphism and up to homotopy equivalence. The ﬁrst turns out to coincide with Al Amrani’s classiﬁcation up to isomorphism of algebraic varieties, and the second follows from our proof that the Mislin genus of any weighted projective space is rigid.

AB - We obtain two classiﬁcations of complex weighted projective spaces, up to homeomorphism and up to homotopy equivalence. The ﬁrst turns out to coincide with Al Amrani’s classiﬁcation up to isomorphism of algebraic varieties, and the second follows from our proof that the Mislin genus of any weighted projective space is rigid.

KW - Classification problem, homeomorphism, homotopy equivalence, weighted projective space

M3 - Working paper

BT - Classifying weighted projective spaces

CY - arXiv.org

ER -

Classifying weighted projective spaces

Abstract

Keywords

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Cite this