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Brill-Noether loci for divisors on irregular varieties | | Margarida Mendes Lopes
; Rita Pardini
; Gian Pietro Pirola
; | | Date: |
29 Dec 2011 | | Abstract: | For a projective variety X, a line bundle L on X and r a natural number we
consider the r-th Brill-Noether locus W^r(L,X):={etain
Pic^0(X)|h^0(L+eta)geq r+1}: we describe its natural scheme structure and
compute the Zariski tangent space. If X is a smooth surface of maximal Albanese
dimension and C is a curve on X, we define a Brill-Noether number
ho(C, r)
and we prove, under some mild additional assumptions, that if
ho(C, r) is non
negative then W^r(C,X) is nonempty of dimension bigger or equal to
ho(C,r).
As an application, we derive lower bounds for h^0(K_D) for a divisor D that
moves linearly on a smooth projective variety X of maximal Albanese dimension
and inequalities for the numerical invariants of curves that do not move
linearly on a surface of maximal Albanese dimension. | | Source: | arXiv, 1112.6357 | | Services: | Forum | Review | PDF | Favorites | |
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