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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.
HOLOMORPHIC EMBEDDINGS OF STEIN SPACES IN INFINITE-DIMENSIONAL PROJECTIVE SPACES
BALLICO E. Korean Mathematical Society 2005 대한수학회지 Vol.42 No.1
Lpt X be a reduced Stein space and L a holomorphic line bundle on X. L is spanned by its global sections and the associated holomorphic map $h_L\;:\;X{\to}P(H^0(X, L)^{\ast})$ is an embedding. Choose any locally convex vector topology ${\tau}\;on\;H^0(X, L)^{\ast}$ stronger than the weak-topology. Here we prove that $h_L(X)$ is sequentially closed in $P(H^0(X, L)^{\ast})$ and arithmetically Cohen -Macaulay. i.e. for all integers $k{\ge}1$ the restriction map ${\rho}_k\;:\;H^0(P(H^0(X, L)^{\ast}),\;O_{P(H^0(X, L)^{\ast})}(k)){\to}H^0(h_L(X),O_{hL_(X)}(k)){\cong}H^0(X, L^{\otimes{k}})$ is surjective.
ON THE ORDER OF SPECIALITY OF A SIMPLE, SPECIAL, AND COMPLETE LINEAR SYSTEM ON A CURVE
Ballico, Edoardo,Homma, Masaaki,Ohbuchi, Akira Korean Mathematical Society 2002 대한수학회지 Vol.39 No.4
The order of speciality of an ample invertible Sheaf L on a curve is the least integer m so that $L^{ m}$ is nonspecial. There is a reasonable upper bound of the order of speciality for a simple invertible sheaf in terms of its degree and projective dimension. We study the case where it reaches the upper bound. Moreover we for mulate Castelnuovo's genus bound involving the order of speciality.ality.
LINEARLY DEPENDENT AND CONCISE SUBSETS OF A SEGRE VARIETY DEPENDING ON k FACTORS
Ballico, Edoardo Korean Mathematical Society 2021 대한수학회보 Vol.58 No.1
We study linearly dependent subsets with prescribed cardinality s of a multiprojective space. If the set S is a circuit, there is an upper bound on the number of factors of the minimal multiprojective space containing S. B. Lovitz gave a sharp upper bound for this number. If S has higher dependency, this may be not true without strong assumptions (and we give examples and suitable assumptions). We describe the dependent subsets S with #S = 6.
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.
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 $g{\geq}4{\gamma}+2{\geq}10$.