Anticanonical divisors of a moduli space of parabolic vector bundles of half weight on ℙ 1
Asian J. Math., Tome 8 (2004) no. 1, p. 395-408 / Harvested from Project Euclid
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Let ℳ0 [resp. ℳ1] be a coarse moduli space of rank 2 semistable vector bundles of even [resp. odd] degree with fixed determinant on a smooth projective curve X. The Picard group is infinite cyclic . Let L be the ample generator. The dimension of a vector space H0(ℳi, Lℳ) (i = 0, 1) is given by the Verlinde formula. For small m > 0, the meaning of this dimension can be explained in the framework of algebraic geometry. For example, we have ¶ dimH0(ℳ0, L) = 2g, ¶ where g is the genus of X. On the other hand, we have ¶ dimH0(Jac(X),O(2ϴ)) = 2g. ¶ In fact we have a natural isomorphism between these two vector spaces (See [1]). In [2], the meaning of the two equations ¶ dimH0(ℳ0, L2) = 2g-1(2g + 1) ¶ dimH0(ℳ1, L) = 2g-1(2g - 1) ¶ are clarified. The above dimensions are the number of even or odd theta characterictics on X. Beauville associated to an even [resp. odd] theta characterictic κ a divisor Dκ on ℳ0 [resp. ℳ1] that can be described from a moduli-theoretic viewpoint, and proved that they form a basis of H0(ℳ0, L2) [resp. H0(ℳ1, L)]. In [13], two vector spaces H0(ℳ0, L4) and H0(ℳ1, L2) are considered. In [15], Pauly deals with a parabolic case. ¶ The purpose of this paper is to carry out a similar study for a moduli space ℳ Par(ℙ1; I) of rank 2 semistable parabolic vector bundles with half weights of degree zero on ℙ1.
Publié le : 2004-09-14
Classification:  
@article{1098300998,
     author = {Abe
, Takeshi},
     title = {Anticanonical divisors of a moduli space of
parabolic vector bundles of half weight on P
<sup>1</sup>},
     journal = {Asian J. Math.},
     volume = {8},
     number = {1},
     year = {2004},
     pages = { 395-408},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1098300998}
}

Abe
, Takeshi. Anticanonical divisors of a moduli space of
parabolic vector bundles of half weight on ℙ
1. Asian J. Math., Tome 8 (2004) no. 1, pp.  395-408. http://gdmltest.u-ga.fr/item/1098300998/