TY - CONF

T1 - Polarization types of isogenous Prym-Tyurin varieties

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

KW - Prym-Tyurin varieties

KW - isogeny

KW - polarization type

KW - Prym varieties

KW - Prym-Tyurin varieties

KW - isogeny

KW - polarization type

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

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

M3 - Other

SP - 147

EP - 174

ER -