6533b7d0fe1ef96bd125b8f9
RESEARCH PRODUCT
Triple planes with $p_g=q=0$
Daniele FaenziFrancesco PolizziJean Vallèssubject
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)Mathematicscoversdescription
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.
| year | journal | country | edition | language |
|---|---|---|---|---|
| 2019-01-01 |