The decomposition groups of plane conics and plane rational cubics

Conics on the Projective Plane

In this paper, we discuss a special property of conics on the projective plane and answer questions in enumerative algebraic geometry such as ”How many points determine a conic?” and ”How many conics do we expect to pass through m points and tangent to n lines?”

The Enumerative Geometry of Plane Cubics. I: Smooth Cubics

We construct a variety of complete plane cubics by a sequence of five blow-ups over P9 . This enables us to translate the problem of computing characteristic numbers for a family of plane cubics into one of computing five Segre classes, and to recover classic enumerative results of Zeuthen and Maillard.

Cremona Transformations, Surface Automorphisms, and Plane Cubics

Every automorphism of the complex projective plane P2 is linear and therefore behaves quite simply when iterated. It is natural to seek other rational complex surfaces—for instance, those obtained from P2 by successive blowing up—that admit automorphisms with more interesting dynamics. Until recently, very few examples with positive entropy seem to have been known (see e.g. the introduction to ...

Plane Conics in Algebraic Geometry

We first examine points and lines within projective spaces. Then we classify affine conics based on the classification of projective conics. Based on the parametrization of conics, we also prove two easy cases of Bézout’s Theorem. In the end we turn to the discussion of the space of conics and the notion of pencils of conics.

Representing Conics Using the Oriented Projective Plane