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The variety of tangents to rational curves

Record Type:	Electronic resources : Monograph/item
Title/Author:	The variety of tangents to rational curves
Author:	Araujo, Carolina.
Description:	91 p.
Notes:	Adviser: Janos Kollar.
Notes:	Source: Dissertation Abstracts International, Volume: 65-02, Section: B, page: 0774.
Contained By:	Dissertation Abstracts International65-02B.
Subject:	Mathematics.
Online resource:	http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=3123412
ISBN:	049670723X

The variety of tangents to rational curves
Araujo, Carolina.

The variety of tangents to rational curves [electronic resource] - 91 p.

Adviser: Janos Kollar.

Thesis (Ph.D.)--Princeton University, 2004.

In this dissertation we investigate the geometry of uniruled varieties by studying minimal covering families of rational curves on them. Our main tool is the variety of tangent directions to rational curves of minimal degree passing through a general point. We provide two applications of this theory. First, we give a unified geometric proof of several characterizations of Pn in terms of positivity properties of the tangent bundle. Second, we provide a method of constructing very free curves of low degree on Fano varieties with Picard number 1.

ISBN: 049670723XSubjects--Topical Terms:

184409
Mathematics.

The variety of tangents to rational curves
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520 # $a In this dissertation we investigate the geometry of uniruled varieties by studying minimal covering families of rational curves on them. Our main tool is the variety of tangent directions to rational curves of minimal degree passing through a general point. We provide two applications of this theory. First, we give a unified geometric proof of several characterizations of Pn in terms of positivity properties of the tangent bundle. Second, we provide a method of constructing very free curves of low degree on Fano varieties with Picard number 1.
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