Some Remarks on Prym-Tyurin Varieties

Parigi, Giuliano. "Some Remarks on Prym-Tyurin Varieties." Bollettino dell'Unione Matematica Italiana 10-B.3 (2007): 1055-1069. <http://eudml.org/doc/290431>.

@article{Parigi2007,
abstract = {The aims of the present paper can be described as follows: a) In [2] Beauville showed that if some endomorphism $u$ a Jacobian $J(C)$ has connected kernel, the principal polarization on $J(C)$ induces a multiple of the principal polarization on the image of $u$. We reformulate and complete this theorem proving "constructively" the following: Theorem. Let $Z \subset J(C)$ be an abelian subvariety and $Y$ its complementary variety. $Z$ is a Prym-Tyurin variety with respect to $J(C)$ if and only if the following sequence $0 \to Y \hookrightarrow J(C) \to Z \to 0$ is exact. b) In [5] Izadi set the question whether every p.p.a.v. is a Prym-Tyurin variety for a symmetric fixed point free correspondence. In this work a contribution to a possible negative answer to this question is provided by building a classical Prym-Tyurin variety explicitly, but this variety can never be defined through a fixed point free correspondence.},
author = {Parigi, Giuliano},
journal = {Bollettino dell'Unione Matematica Italiana},
language = {eng},
month = {10},
number = {3},
pages = {1055-1069},
publisher = {Unione Matematica Italiana},
title = {Some Remarks on Prym-Tyurin Varieties},
url = {http://eudml.org/doc/290431},
volume = {10-B},
year = {2007},
}

TY - JOUR
AU - Parigi, Giuliano
TI - Some Remarks on Prym-Tyurin Varieties
JO - Bollettino dell'Unione Matematica Italiana
DA - 2007/10//
PB - Unione Matematica Italiana
VL - 10-B
IS - 3
SP - 1055
EP - 1069
AB - The aims of the present paper can be described as follows: a) In [2] Beauville showed that if some endomorphism $u$ a Jacobian $J(C)$ has connected kernel, the principal polarization on $J(C)$ induces a multiple of the principal polarization on the image of $u$. We reformulate and complete this theorem proving "constructively" the following: Theorem. Let $Z \subset J(C)$ be an abelian subvariety and $Y$ its complementary variety. $Z$ is a Prym-Tyurin variety with respect to $J(C)$ if and only if the following sequence $0 \to Y \hookrightarrow J(C) \to Z \to 0$ is exact. b) In [5] Izadi set the question whether every p.p.a.v. is a Prym-Tyurin variety for a symmetric fixed point free correspondence. In this work a contribution to a possible negative answer to this question is provided by building a classical Prym-Tyurin variety explicitly, but this variety can never be defined through a fixed point free correspondence.
LA - eng
UR - http://eudml.org/doc/290431
ER -