Polarization types of isogenous Prym-Tyurin varieties

Lange, H

Risultato della ricerca: Paper

Abstract

Let p:C-->Y be a covering of smooth, projective curves which is a composition of \pi:C-->C'' of degree 2 and g:C''-->Y of degree n. Let f:X-->Y be the covering of degree 2^n, where the curve X parametrizes the liftings in C^{(n)} of the fibers of g:C''-->Y. Let P(X,\delta) be the associated Prym-Tyurin variety, known to be isogenous to the Prym variety P(C,C''). Most of the results in the paper focus on calculating the polarization type of the restriction of the canonical polarization of JX on P(X,\delta). We obtain the polarization type when n=3. When Y=P^1 we conjecture that P(X,\delta) is isomorphic to the dual of the Prym variety P(C,C''). This was known when n=2, we prove it when n=3, and for arbitrary n if \pi:C-->C'' is \''{e}tale. Similar results are obtained for some other types of coverings.
Lingua originaleEnglish
Stato di pubblicazionePublished - 2008

Fingerprint

Prym Varieties
Covering
Polarization
Pi
Curve
Isomorphic
Fiber
Restriction
Arbitrary

Cita questo

Polarization types of isogenous Prym-Tyurin varieties. / Lange, H.

2008.

Risultato della ricerca: Paper

@conference{6e41bfa66ce9422684b9851124a9b562,
title = "Polarization types of isogenous Prym-Tyurin varieties",
abstract = "Let p:C-->Y be a covering of smooth, projective curves which is a composition of \pi:C-->C'' of degree 2 and g:C''-->Y of degree n. Let f:X-->Y be the covering of degree 2^n, where the curve X parametrizes the liftings in C^{(n)} of the fibers of g:C''-->Y. Let P(X,\delta) be the associated Prym-Tyurin variety, known to be isogenous to the Prym variety P(C,C''). Most of the results in the paper focus on calculating the polarization type of the restriction of the canonical polarization of JX on P(X,\delta). We obtain the polarization type when n=3. When Y=P^1 we conjecture that P(X,\delta) is isomorphic to the dual of the Prym variety P(C,C''). This was known when n=2, we prove it when n=3, and for arbitrary n if \pi:C-->C'' is \''{e}tale. Similar results are obtained for some other types of coverings.",
keywords = "Prym varieties; Prym-Tyurin varieties; polarization type; isogeny",
author = "{Lange, H} and Vassil Kanev",
year = "2008",
language = "English",

}

TY - CONF

T1 - Polarization types of isogenous Prym-Tyurin varieties

AU - Lange, H

AU - Kanev, Vassil

PY - 2008

Y1 - 2008

N2 - Let p:C-->Y be a covering of smooth, projective curves which is a composition of \pi:C-->C'' of degree 2 and g:C''-->Y of degree n. Let f:X-->Y be the covering of degree 2^n, where the curve X parametrizes the liftings in C^{(n)} of the fibers of g:C''-->Y. Let P(X,\delta) be the associated Prym-Tyurin variety, known to be isogenous to the Prym variety P(C,C''). Most of the results in the paper focus on calculating the polarization type of the restriction of the canonical polarization of JX on P(X,\delta). We obtain the polarization type when n=3. When Y=P^1 we conjecture that P(X,\delta) is isomorphic to the dual of the Prym variety P(C,C''). This was known when n=2, we prove it when n=3, and for arbitrary n if \pi:C-->C'' is \''{e}tale. Similar results are obtained for some other types of coverings.

AB - Let p:C-->Y be a covering of smooth, projective curves which is a composition of \pi:C-->C'' of degree 2 and g:C''-->Y of degree n. Let f:X-->Y be the covering of degree 2^n, where the curve X parametrizes the liftings in C^{(n)} of the fibers of g:C''-->Y. Let P(X,\delta) be the associated Prym-Tyurin variety, known to be isogenous to the Prym variety P(C,C''). Most of the results in the paper focus on calculating the polarization type of the restriction of the canonical polarization of JX on P(X,\delta). We obtain the polarization type when n=3. When Y=P^1 we conjecture that P(X,\delta) is isomorphic to the dual of the Prym variety P(C,C''). This was known when n=2, we prove it when n=3, and for arbitrary n if \pi:C-->C'' is \''{e}tale. Similar results are obtained for some other types of coverings.

KW - Prym varieties; Prym-Tyurin varieties; polarization type; isogeny

UR - http://hdl.handle.net/10447/40213

UR - http://arxiv.org/abs/0707.0364

M3 - Paper

ER -