Another Proof of Segre's Theorem about Ovals

• Published in 2013
• Added on 2015-09-29

In 1955 B. Segre showed that any oval in a projective plane over a finite field of odd order is a conic. His proof constructs a conic which matches the oval in some points, and then shows that it actually coincides with the oval. Here we give another proof. We describe the oval by a possibly high degree polynomial, and then show that the degree is actually 2.

Links

• http://arxiv.org/abs/1311.3082
• http://arxiv.org/pdf/1311.3082v1

Other information

BibTeX entry

@article{Muller2013,
	key = {Muller2013},
	type = {article},
	title = {Another Proof of Segre's Theorem about Ovals},
	author = {M{\"{u}}ller, Peter},
	abstract = {In 1955 B. Segre showed that any oval in a projective plane over a finite field of odd order is a conic. His proof constructs a conic which matches the oval in some points, and then shows that it actually coincides with the oval. Here we give another proof. We describe the oval by a possibly high degree polynomial, and then show that the degree is actually 2.},
	comment = {},
	date_added = {2015-09-29},
	date_published = {2013-11-01},
	urls = {http://arxiv.org/abs/1311.3082,http://arxiv.org/pdf/1311.3082v1},
	collections = {About proof},
	month = {nov},
	pages = 2,
	url = {http://arxiv.org/abs/1311.3082 http://arxiv.org/pdf/1311.3082v1},
	year = 2013,
	archivePrefix = {arXiv},
	eprint = {1311.3082},
	primaryClass = {math.NT},
	urldate = {2015-09-29}
}