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Projektionen von glatten Flächen in den P⁴

Title data

Bauer, Ingrid:
Projektionen von glatten Flächen in den P⁴.
Bonn , 1994 . - 92 p. - (Bonner mathematische Schriften ; 260 )


Abstract in another language

The main result of this dissertation is the classification of smooth surfaces in P5 that do not have a trisecant line through a general point on the surface. A corollary is the confirmation of a conjecture by Van de Ven that there are only finitely many smooth surfaces in P4 that are obtained by projecting a smooth surface in P5 from a point on the surface. The classification is obtained by an effective use of a trisecant formula of Le Barz, which counts the number of trisecant lines to a surface in P5 which meets a general plane in P5, when this is finite. Together with the double point formula for surfaces in P4, it quickly leads to the bound of 11 for the degree of the surface. The argument becomes effective by some precise geometric conditions, which indicate exactly when and how the numerical formulas apply.
Next, the classification of smooth surfaces of degree at most 10 in P4 is used to make a precise list of surfaces with the above property. In each case a precise description of the union of trisecants is given. In fact the union of trisecants consists of lines on the surface and planes meeting the surface in a curve. Some cases are particularly delicate, since some surfaces have a pencil of plane curves of degree at least 3 while a general smooth deformation does not. The author makes use of a long list of techniques and tricks of the trade to obtain the result.

Further data

Item Type: Book / Monograph
Additional notes: Zugl.: Bonn, Univ., Diss., 1992
Subject classification: Mathematics Subject Classification Code: 14J10 (14M07 14N10)
Institutions of the University: Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics > Professor Algebraic Geometry > Professor Algebraic Geometry - Univ.-Prof. Dr. Ingrid Bauer
Result of work at the UBT: No
DDC Subjects: 500 Science > 510 Mathematics
Date Deposited: 14 Jun 2021 11:15
Last Modified: 14 Jun 2021 11:15
URI: https://eref.uni-bayreuth.de/id/eprint/65853