NDLI: On the space of projective curves of maximal regularity

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On the space of projective curves of maximal regularity

Content Provider	Springer Nature Link
Author	Lee, Wanseok Park, Euisung Chung, Kiryong
Copyright Year	2016
Abstract	Let $$\Gamma _{r,d}$$ be the space of smooth rational curves of degree d in $${\mathbb {P}}^r$$ of maximal regularity. Then the automorphism group $$\mathrm{Aut}({\mathbb {P}}^r)=\mathrm{PGL}(r+1)$$ acts naturally on $$\Gamma _{r,d}$$ and thus the quotient $$\Gamma _{r,d}/ \mathrm{PGL}(r+1)$$ classifies those rational curves up to projective motions. In this paper, we show that $$\Gamma _{r,d}$$ is an irreducible variety of dimension $$3d+r^2-r-1$$ . The main idea of the proof is to use the canonical form of rational curves of maximal regularity which is given by the $$(d-r+2)$$ -secant line. Also, through the geometric invariant theory, we discuss how to give a scheme structure on the $$\mathrm{PGL}(r+1)$$ -orbits of rational curves.
Ending Page	518
Page Count	14
Starting Page	505
File Format	PDF
ISSN	00252611
e-ISSN	14321785
Journal	Manuscripta Mathematica
Issue Number	3-4
Volume Number	151
Language	English
Publisher	Springer Berlin Heidelberg
Publisher Date	2016-05-02
Publisher Place	Berlin, Heidelberg
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Geometry Questions of classical algebraic geometry Topological Groups, Lie Groups Special curves and curves of low genus Stacks and moduli problems Calculus of Variations and Optimal Control; Optimization Algebraic Geometry Mathematics Number Theory
Content Type	Text
Resource Type	Article
Subject	Mathematics

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