• Corpus ID: 119136896

Incidences of lines in $P^3$ and the arithmetic genus of curves

@article{Kollar2014IncidencesOL,
  title={Incidences of lines in \$P^3\$ and the arithmetic genus of curves},
  author={J'anos Koll'ar},
  journal={arXiv: Algebraic Geometry},
  year={2014}
}
  • J. Koll'ar
  • Published 16 April 2014
  • Mathematics
  • arXiv: Algebraic Geometry
Guth and Katz proved that, as conjectured by Elekes and Sharir, $m$ lines in 3-space have at most constant times $ m^{3/2}$ intersection points, aside from some obvious counter examples. We give an explicit bound for the constant, using the arithmetic genus of the union of the lines. 

References

SHOWING 1-8 OF 8 REFERENCES

Counting lines on surfaces

This paper deals with surfaces with many lines. It is well-known that a cubic contains 27 of them and that the maximal number for a quartic is 64. In higher degree the question remains open. Here we

Basic algebraic geometry

The second volume of Shafarevich's introductory book on algebraic geometry focuses on schemes, complex algebraic varieties and complex manifolds. As with first volume the author has revised the text

Simple groups of Lie type

Partial table of contents: The Classical Simple Groups. Weyl Groups. Simple Lie Algebras. The Chevalley Groups. Unipotent Subgroups. The Diagonal and Monomial Subgroups. The Bruhat Decomposition.

Incidences in three dimensions and distinct distances in the plane

This work adapts the recent new algebraic analysis technique of Guth and Katz, as well as further developed by Elekes et al.

Point–Line Incidences in Space

These bounds are smaller than the tight Szemerédi–Trotter bound for point–line incidences in $\reals^2$, unless both bounds are linear.

Introduction to commutative algebra

* Introduction * Rings and Ideals * Modules * Rings and Modules of Fractions * Primary Decomposition * Integral Dependence and Valuations * Chain Conditions * Noetherian Rings * Artin Rings *