scholarly journals Ramification points of Seiberg-Witten curves

2011 ◽  
Vol 2011 (7) ◽  
Author(s):  
Chan Y. Park
Keyword(s):  
2004 ◽  
Vol 46 (1-2) ◽  
pp. 13-15
Author(s):  
E. Ballico ◽  
C. Keem

Author(s):  
Paola Frediani ◽  
Gian Paolo Grosselli

We study Shimura curves of PEL type in the space of polarized abelian varieties [Formula: see text] generically contained in the ramified Prym locus. We generalize to ramified double covers, the construction done in [E. Colombo, P. Frediani, A. Ghigi and M. Penegini, Shimura curves in the Prym locus, Commun. Contemp. Math. 21(2) (2019) 1850009] in the unramified case and in the case of two ramification points. Namely, we construct families of double covers which are compatible with a fixed group action on the base curve. We only consider the case of one-dimensional families and where the quotient of the base curve by the group is [Formula: see text]. Using computer algebra we obtain 184 Shimura curves contained in the (ramified) Prym loci.


2002 ◽  
Vol 11 (07) ◽  
pp. 1063-1075 ◽  
Author(s):  
SERGEI NATANZON ◽  
BORIS SHAPIRO ◽  
ALEK VAINSHTEIN

To any real rational function with generic ramification points we assign a combinatorial object, called a garden, which consists of a weighted labeled directed planar chord diagram and of a set of weighted rooted trees each corresponding to a face of the diagram. We prove that any garden corresponds to a generic real rational function, and that equivalent functions have equivalent gardens.


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