# Some Remarks on Prym-Tyurin Varieties

Bollettino dell'Unione Matematica Italiana (2007)

- Volume: 10-B, Issue: 3, page 1055-1069
- ISSN: 0392-4041

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topParigi, 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 -

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