论文标题
在Prym基因座和测量学的Jacobian基因座上
On the Jacobian locus in the Prym locus and geodesics
论文作者
论文摘要
在本文中，我们考虑jacobian likus $ \上线{j_g} $和prym locus $ \ operline {p_ {p_ {g+1}} $，在Moduli space $ a_g $ a_g $ a_g $ a_g $ a_g $ a_g $ a $ g $ g $ g $ g $ g $ g \ geq 7 $的$ g \ geq的;在Beauville介绍的广义Prym品种理论提供的包含下，\ edline {p_ {p_ {g+1}} $。更确切地说，我们研究了$ a_g $的siegel度量的某些地质曲线，从jacobian品种$ [jc] \ in m_g $ in m_g $的a_g $ [c] \ in m_g $，并且在t _ {[jc] j_g $ in t toriende $ζ\ in Direction $ζ\。我们证明，对于一般的$ JC $，此类的任何地理都不会包含在$ \ overline {J_G} $中，甚至在$ \ overline {p_ {g+1}} $中，如果$序列$ k <\ cliff c-3 $，则$ \ cliff c $ \ cliff c $ ex $ cliff c $ ex $ c $ c $ c $ c $ c $ c $ c $ c $ c $ c $ c。
In the paper we consider the Jacobian locus $\overline{J_g}$ and the Prym locus $\overline{P_{g+1}}$, in the moduli space $A_g$ of principally polarized abelian varieties of dimension $g$, for $g\geq 7$, and we study the extrinsic geometry of $\overline{J_g}\subset \overline{P_{g+1}}$, under the inclusion provided by the theory of generalized Prym varieties as introduced by Beauville. More precisely, we study certain geodesic curves with respect to the Siegel metric of $A_g$, starting at a Jacobian variety $[JC]\in A_g$ of a curve $[C]\in M_g$ and with direction $ζ\in T_{[JC]}J_g$. We prove that for a general $JC$, any geodesic of this kind is not contained in $\overline{J_g}$ and even in $\overline{P_{g+1}}$, if $ζ$ has rank $k<\Cliff C-3$, where $\Cliff C$ denotes the Clifford index of $C$.
