CUBIC EQUATIONS FOR THE HYPERELLIPTIC LOCUS
Asian J. Math., Tome 8 (2004) no. 1, p. 161-172 / Harvested from Project Euclid
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We prove a conjecture from [BK2] that the multi-dimensional vector addition formula for Baker-Akhiezer functions obtained there characterizes Jacobians among principally polarized abelian varieties. We also show that this addition formula is equivalent to Gunning's multisecant formula for the Kummer variety obtained in [Gu2]. ¶ We then use this addition formula to obtain cubic relations among theta functions that characterize the locus of hyperelliptic Jacobians among irreducible abelian varieties. In genus 3 our equations are equivalent to the vanishing of one theta-null, and thus are classical (see [M], [P]), but already for genus 4 they appear to be new.
Publié le : 2004-01-14
Classification:  
@article{1087840914,
     author = {GRUSHEVSKY
, SAMUEL},
     title = {CUBIC EQUATIONS FOR THE HYPERELLIPTIC LOCUS},
     journal = {Asian J. Math.},
     volume = {8},
     number = {1},
     year = {2004},
     pages = { 161-172},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1087840914}
}

GRUSHEVSKY
, SAMUEL. CUBIC EQUATIONS FOR THE HYPERELLIPTIC LOCUS. Asian J. Math., Tome 8 (2004) no. 1, pp.  161-172. http://gdmltest.u-ga.fr/item/1087840914/