2007/07/03 by Vassil Kanev, Herbert Lange, Kanev, Vassil +1
Chemistry · Mathematics · #14H30 #14H40 #14K02 #Algebraic Geometry (math.AG) #Axial and Atropisomeric Chirality Synthesis #FOS: Mathematics #math.AG #msc:14H30 #msc:14H40 #msc:14K02
paper · pdf · doi:10.48550/arxiv.0707.0364
28 pages
arxiv created 2007/07/03 · openalex publication_date 2007/07/03 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Let p:C-->Y be a covering of smooth, projective curves which is a composition of π:C-->C' of degree 2 and g:C'-->Y of degree n. Let f:X-->Y be the covering of degree 2n, where the curve X parametrizes the liftings in C(n) of the fibers of g:C'-->Y. Let P(X,δ) 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,δ). We obtain the polarization type when n=3. When Y=P1 we conjecture that P(X,δ) 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 π:C-->C' is étale. Similar results are obtained for some other types of coverings.