Planar, rational curves over ${\mathbb F}_2$ whose only singularity is a double point

János Kollár

Planar, rational curves over ${\mathbb F}_2$ whose only singularity is a double point

János Kollár

Abstract

We exhibit planar, rational curves of large degree over ${\mathbb F}_2$ that have a unique singular point, which has multiplicity 2. In characteristic 0 such curves exist only for degrees up to $6$.

Planar, rational curves over ${\mathbb F}_2$ whose only singularity is a double point

Abstract

We exhibit planar, rational curves of large degree over

that have a unique singular point, which has multiplicity 2. In characteristic 0 such curves exist only for degrees up to

Paper Structure (2 theorems, 7 equations)

This paper contains 2 theorems, 7 equations.

Key Result

Lemma 2

For the curves $C_{q,r}$ in Example the following hold.

Theorems & Definitions (9)

Example 1
Lemma 2
Example 3
Lemma 4
Remark 5
Remark 6
Remark 7: Connection with ishii2025liftingsidealspositivecharacteristic
Remark 8: Log canonical thresholds
Example 9: Quartic surfaces