0000000000134656

AUTHOR

Jean Vallès

showing 2 related works from this author

Triple planes with $p_g=q=0$

2019

We show that general triple planes with p_g=q=0 belong to at most 12 families, that we call surfaces of type I,..., XII, and we prove that the corresponding Tschirnhausen bundle is direct sum of two line bundles in cases I, II, III, whereas is a rank 2 Steiner bundle in the remaining cases. We also provide existence results and explicit constructions for surfaces of type I,..., VII, recovering all classical examples and discovering several new ones. In particular, triple planes of type VII provide counterexamples to a wrong claim made in 1942 by Bronowski.

Discrete mathematicsSteiner bundleApplied MathematicsGeneral Mathematics010102 general mathematicsprojective varietiesspaceadjunction theorysurfaces01 natural sciences14E20bundlesunstable hyperplanesMathematics - Algebraic GeometryTriple plane0103 physical sciencesFOS: Mathematics010307 mathematical physicsarrangements[MATH.MATH-AG]Mathematics [math]/Algebraic Geometry [math.AG]0101 mathematicsMSc: Primary 14E20 14J60Algebraic Geometry (math.AG)Mathematicscovers
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Logarithmic bundles of deformed Weyl arrangements of type $A_2$

2016

We consider deformations of the Weyl arrangement of type $A_2$, which include the extended Shi and Catalan arrangements. These last ones are well-known to be free. We study their sheaves of logarithmic vector fields in all other cases, and show that they are Steiner bundles. Also, we determine explicitly their unstable lines. As a corollary, some counter-examples to the shift isomorphism problem are given.

Pure mathematicsLogarithmic sheavesLogarithmMSC: 52C35 14F05 32S22General Mathematics010102 general mathematicsType (model theory)Weyl arrangements01 natural sciences[ MATH.MATH-AG ] Mathematics [math]/Algebraic Geometry [math.AG]Mathematics - Algebraic GeometryComputer Science::GraphicsCorollary0103 physical sciencesFOS: Mathematics010307 mathematical physicsIsomorphism[MATH.MATH-AG]Mathematics [math]/Algebraic Geometry [math.AG]0101 mathematicsRoot systemsLine arrangementsMSC 52C35 14F05 32S22Algebraic Geometry (math.AG)Mathematics
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