0000000000116629

AUTHOR

Francesco Malaspina

0000-0002-6740-6051

showing 3 related works from this author

Surfaces of minimal degree of tame representation type and mutations of Cohen–Macaulay modules

2017

We provide two examples of smooth projective surfaces of tame CM type, by showing that any parameter space of isomorphism classes of indecomposable ACM bundles with fixed rank and determinant on a rational quartic scroll in projective 5-space is either a single point or a projective line. For surfaces of minimal degree and wild CM type, we classify rigid Ulrich bundles as Fibonacci extensions. For the rational normal scrolls S(2,3) and S(3,3), a complete classification of rigid ACM bundles is given in terms of the action of the braid group in three strands.

[ MATH ] Mathematics [math]Pure mathematicsFibonacci numberGeneral MathematicsType (model theory)Rank (differential topology)Commutative Algebra (math.AC)01 natural sciencesMathematics - Algebraic GeometryACM bundlesVarieties of minimal degreeMathematics::Algebraic Geometry0103 physical sciencesFOS: MathematicsMathematics (all)Rings0101 mathematics[MATH]Mathematics [math]Algebraic Geometry (math.AG)MathematicsDiscrete mathematics14F05 13C14 14J60 16G60010102 general mathematicsVarietiesMCM modulesACM bundles; MCM modules; Tame CM type; Ulrich bundles; Varieties of minimal degree; Mathematics (all)Ulrich bundlesMathematics - Commutative AlgebraQuintic functionElliptic curveTame CM typeProjective lineBundles010307 mathematical physicsIsomorphismIndecomposable moduleMSC: 14F05; 13C14; 14J60; 16G60
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Rank two aCM bundles on the del Pezzo fourfold of degree 6 and its general hyperplane section

2018

International audience; In the present paper we completely classify locally free sheaves of rank 2 with vanishing intermediate cohomology modules on the image of the Segre embedding $\mathbb{P}^2$ x $\mathbb{P}^2 \subseteq \mathbb{P}^8$ and its general hyperplane sections.Such a classification extends similar already known results regarding del Pezzo varieties with Picard numbers 1 and 3 and dimension at least 3.

Algebra and Number TheoryDegree (graph theory)Image (category theory)010102 general mathematicsDimension (graph theory)MSC: Primary 14J60 ; secondary 14J45Hyperplane sectionRank (differential topology)01 natural sciencesCohomologySegre embedding[ MATH.MATH-AG ] Mathematics [math]/Algebraic Geometry [math.AG]CombinatoricsAlgebraMathematics::Algebraic GeometryHyperplane0103 physical sciences010307 mathematical physics[MATH.MATH-AG]Mathematics [math]/Algebraic Geometry [math.AG]0101 mathematicsMathematics
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Moduli spaces of rank two aCM bundles on the Segre product of three projective lines

2016

Let P^n be the projective space of dimension n on an algebraically closed field of characteristic 0 and F be the image of the Segre embedding of P^1xP^1xP^1 inside P^7. In the present paper we deal with the moduli spaces of locally free sheaves E on F of rank 2 with h^i(F,E(t))=0 for i=1,2 and each integer t.

14J60 14J45 14D20[MATH.MATH-AC]Mathematics [math]/Commutative Algebra [math.AC]Rank (differential topology)Commutative Algebra (math.AC)01 natural sciences[ MATH.MATH-AC ] Mathematics [math]/Commutative Algebra [math.AC]CombinatoricsMathematics - Algebraic GeometryMathematics::Algebraic Geometry0103 physical sciencesFOS: Mathematics0101 mathematicsProjective testAlgebraic Geometry (math.AG)MathematicsAlgebra and Number TheoryImage (category theory)010102 general mathematicsMathematics - Commutative Algebra16. Peace & justice[ MATH.MATH-AG ] Mathematics [math]/Algebraic Geometry [math.AG]Moduli spaceSegre embeddingMSC: Primary: 14J60; secondary: 14J45; 14D20Product (mathematics)[MATH.MATH-AG]Mathematics [math]/Algebraic Geometry [math.AG]010307 mathematical physicsJournal of Pure and Applied Algebra
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