Complete Families of Linearly Non-degenerate Rational Curves

Autor:	Matthew DeLand
Rok vydání:	2011
Předmět:	General method Degree (graph theory) General Mathematics Degenerate energy levels Columbia university Base (topology) Cohomology Moduli Combinatorics Mathematics - Algebraic Geometry Grassmannian FOS: Mathematics Algebraic Geometry (math.AG) Mathematics
Zdroj:	Canadian Mathematical Bulletin. 54:430-441
ISSN:	1496-4287 0008-4395
Popis:	We prove that a complete family of linearly non-degenerate rational curves of degree $e > 2$ in $\mathbb{P}^n$ has at most $n-1$ moduli. For $e = 2$ we prove that such a family has at most $n$ moduli. It is unknown whether or not this is the best possible result. The general method involves exhibiting a map from the base of a family $X$ to the Grassmaninian of $e$-planes in $\mathbb{P}^n$ and analyzing the resulting map on cohomology. 14 pages
Databáze:	OpenAIRE
Externí odkaz:	https://explore.openaire.eu/search/publication?articleId=doi_dedup___::14ba6fb5e823dd30d536a769fe6aa6ee https://doi.org/10.4153/cmb-2011-021-2 Zobrazit plný text záznamu