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The Kodaira dimension of the moduli space of Prym varieties

Gavril Farkas, Katharina Ludwig (2010)

Journal of the European Mathematical Society

We study the enumerative geometry of the moduli space ℛ g of Prym varieties of dimension g - 1 . Our main result is that the compactication of ℛ g is of general type as soon as g > 13 and g is different from 15. We achieve this by computing the class of two types of cycles on ℛ g : one defined in terms of Koszul cohomology of Prym curves, the other defined in terms of Raynaud theta divisors associated to certain vector bundles on curves. We formulate a Prym–Green conjecture on syzygies of Prym-canonical curves....

Very ampleness of multiples of principal polarization on degenerate Abelian surfaces.

Alessandro Arsie (2005)

Revista Matemática Complutense

Quite recently, Alexeev and Nakamura proved that if Y is a stable semi-Abelic variety (SSAV) of dimension g equipped with the ample line bundle OY(1), which deforms to a principally polarized Abelian variety, then OY(n) is very ample as soon as n ≥ 2g + 1, that is n ≥ 5 in the case of surfaces. Here it is proved, via elementary methods of projective geometry, that in the case of surfaces this bound can be improved to n ≥ 3.

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