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aCM sheaves of pure rank two on reducible hyperquadrics
Ballico, Edoardo,Huh, Sukmoon,Pons-Llopis, Joan Academic Press 2017 Journal of algebra Vol.489 No.-
<P><B>Abstract</B></P> <P>We classify a special type of arithmetically Cohen–Macaulay sheaves of rank two on reducible and reduced quadric hypersurfaces. As a consequence we show that a reducible and reduced quadric surface is of wild type.</P>
Footnote to a manuscript by Gwena and Teixidor i Bigas
Edoardo Ballico,Claudio Fontanari 대한수학회 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>
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 $g{\geq}4{\gamma}+2{\geq}10$.
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.
BEYOND THE CACTUS RANK OF TENSORS
Ballico, Edoardo Korean Mathematical Society 2018 대한수학회보 Vol.55 No.5
We study additive decompositions (and generalized additive decompositions with a zero-dimensional scheme instead of a finite sum of rank 1 tensors), which are not of minimal degree (for sums of rank 1 tensors with more terms than the rank of the tensor, for a zero-dimensional scheme a degree higher than the cactus rank of the tensor). We prove their existence for all degrees higher than the rank of the tensor and, with strong assumptions, higher than the cactus rank of the tensor. Examples show that additional assumptions are needed to get the minimally spanning scheme of degree cactus +1.
Beyond the cactus rank of tensors
Edoardo Ballico 대한수학회 2018 대한수학회보 Vol.55 No.5
We study additive decompositions (and generalized additive decompositions with a zero-dimensional scheme instead of a finite sum of rank $1$ tensors), which are not of minimal degree (for sums of rank $1$ tensors with more terms than the rank of the tensor, for a zero-dimensional scheme a degree higher than the cactus rank of the tensor). We prove their existence for all degrees higher than the rank of the tensor and, with strong assumptions, higher than the cactus rank of the tensor. Examples show that additional assumptions are needed to get the minimally spanning scheme of degree cactus $+1$.
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.