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UNIFORMITY OF HOLOMORPHIC VECTOR BUNDLES ON INFINITE-DIMENSIONAL FLAG MANIFOLDS
Ballico, E. Korean Mathematical Society 2003 대한수학회보 Vol.40 No.1
Let V be a localizing infinite-dimensional complex Banach space. Let X be a flag manifold of finite flags either of finite codimensional closed linear subspaces of V or of finite dimensional linear subspaces of V. Let E be a holomorphic vector bundle on X with finite rank. Here we prove that E is uniform, i.e. that for any two lines $D_1$ R in the same system of lines on X the vector bundles E$\mid$D and E$\mid$R have the same splitting type.
BRILL-NOETHER THEORY FOR RANK 1 TORSION FREE SHEAVES ON SINGULAR PROJECTIVE CURVES
Ballico, E. Korean Mathematical Society 2000 대한수학회지 Vol.37 No.3
Let X be an integral Gorenstein projective curve with g:=pa(X) $\geq$ 3. Call $G^r_d$ (X,**) the set of all pairs (L,V) with L$\epsilon$Pic(X), deg(L) = d, V $\subseteq$ H^0$(X,L), dim(V) =r+1 and V spanning L. Assume the existence of integers d, r with 1 $\leq$ r$\leq$ d $\leq$ g-1 such that there exists an irreducible component, , of $G^r_d$(X,**) with dim($\Gamma$) $\geq$ d - 2r and such that the general L$\geq$$\Gamma$ is spanned at every point of Sing(X). Here we prove that dim( ) = d-2r and X is hyperelliptic.
FOOTNOTE TO A MANUSCRIPT BY GWENA AND TEIXIDOR I BIGAS
Ballico, Edoardo,Fontanari, Claudio Korean Mathematical Society 2009 대한수학회보 Vol.46 No.1
Recent work by Gwena and Teixidor i Bigas provides a characteristic-free proof of a part of a previous theorem by one of us, under a stronger numerical assumption. By using an intermediate result from the mentioned manuscript, here we present a simpler, characteristic-free proof of the whole original statement.
Stable Sheaves on a Smooth Quadric Surface with Linear Hilbert Bipolynomials
Ballico, Edoardo,Huh, Sukmoon Hindawi Limited 2014 The Scientific World Journal Vol.2014 No.-
<P>We investigate the moduli spaces of stable sheaves on a smooth quadric surface with linear Hilbert bipolynomial in some special cases and describe their geometry in terms of the locally free resolution of the sheaves.</P>
ON THE GEOMETRY OF BIHYPERELLIPTIC CURVES
Ballico, Edoardo,Casnati, Gianfranco,Fontanari, Claudio Korean Mathematical Society 2007 대한수학회지 Vol.44 No.6
Here we consider bihyperelliptic curves, i.e., double covers of hyperelliptic curves. By applying the theory of quadruple covers, among other things we prove that the bihyperelliptic locus in the moduli space of smooth curves is irreducible and unirational $g{\geq}4{\gamma}+2{\geq}10$.
BRILL-NOETHER DIVISORS ON THE MODULI SPACE OF CURVES AND APPLICATIONS
BALLICO EDOARDO,FONTANARI CLAUDIO Korean Mathematical Society 2005 대한수학회지 Vol.42 No.6
Here we generalize previous work by Eisenbud-Harris and Farkas in order to prove that certain Brill-Noether divisors on the moduli space of curves have distinct supports. From this fact we deduce non-trivial regularity results for a higher co dimensional Brill-Noether locus and for the general $\frac{g+1}{2}$-gonal curve of odd genusg.