6533b7d0fe1ef96bd125a480
RESEARCH PRODUCT
Surfaces of minimal degree of tame representation type and mutations of Cohen–Macaulay modules
Daniele FaenziFrancesco Malaspinasubject
[ 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; 16G60description
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.
| year | journal | country | edition | language |
|---|---|---|---|---|
| 2017-04-13 |