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Interpolation and Vector Bundles on Curves

2015
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Release : 2015
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Book Synopsis Interpolation and Vector Bundles on Curves by : Atanas Valeryev Atanasov

Download or read book Interpolation and Vector Bundles on Curves written by Atanas Valeryev Atanasov. This book was released on 2015. Available in PDF, EPUB and Kindle. Book excerpt: Interpolation is a property of vector bundles on curves closely related to slope stability. The notion is motivated by the deformation theory of curves in projective space incident to given fixed subvarieties. If the normal bundle of a projective curve satisfies interpolation, then curves in the same component of the Hilbert scheme exhibit normal behavior with respect to incident problems.

Interpolation for Normal Bundles of General Curves

2019-02-21 Curves, Algebraic
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Release : 2019-02-21
Genre : Curves, Algebraic
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Book Rating : 89X/5 ( reviews)

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Book Synopsis Interpolation for Normal Bundles of General Curves by : Atanas Atanasov

Download or read book Interpolation for Normal Bundles of General Curves written by Atanas Atanasov. This book was released on 2019-02-21. Available in PDF, EPUB and Kindle. Book excerpt: Given n general points p1,p2,…,pn∈Pr, it is natural to ask when there exists a curve C⊂Pr, of degree d and genus g, passing through p1,p2,…,pn. In this paper, the authors give a complete answer to this question for curves C with nonspecial hyperplane section. This result is a consequence of our main theorem, which states that the normal bundle NC of a general nonspecial curve of degree d and genus g in Pr (with d≥g+r) has the property of interpolation (i.e. that for a general effective divisor D of any degree on C, either H0(NC(−D))=0 or H1(NC(−D))=0), with exactly three exceptions.

Vector Bundles on Algebraic Curves

1990
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Release : 1990
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Book Synopsis Vector Bundles on Algebraic Curves by : Iwona Maria Grzegorczyk

Download or read book Vector Bundles on Algebraic Curves written by Iwona Maria Grzegorczyk. This book was released on 1990. Available in PDF, EPUB and Kindle. Book excerpt:

Vector Bundles on Curves - New Directions

2006-11-14 Mathematics
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Release : 2006-11-14
Genre : Mathematics
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Book Rating : 013/5 ( reviews)

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Book Synopsis Vector Bundles on Curves - New Directions by : Shrawan Kumar

Download or read book Vector Bundles on Curves - New Directions written by Shrawan Kumar. This book was released on 2006-11-14. Available in PDF, EPUB and Kindle. Book excerpt: The book gives a survey of some recent developments in the theory of bundles on curves arising out of the work of Drinfeld and from insights coming from Theoretical Physics. It deals with: 1. The relation between conformal blocks and generalised theta functions (Lectures by S. Kumar) 2. Drinfeld Shtukas (Lectures by G. Laumon) 3. Drinfeld modules and Elliptic Sheaves (Lectures by U. Stuhler) The latter topics are useful in connection with Langlands programme for function fields. The contents of the book would give a comprehensive introduction of these topics to graduate students and researchers.

Birational Geometry, Rational Curves, and Arithmetic

2013-05-17 Mathematics
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Release : 2013-05-17
Genre : Mathematics
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Book Rating : 82X/5 ( reviews)

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Book Synopsis Birational Geometry, Rational Curves, and Arithmetic by : Fedor Bogomolov

Download or read book Birational Geometry, Rational Curves, and Arithmetic written by Fedor Bogomolov. This book was released on 2013-05-17. Available in PDF, EPUB and Kindle. Book excerpt: ​​​​This book features recent developments in a rapidly growing area at the interface of higher-dimensional birational geometry and arithmetic geometry. It focuses on the geometry of spaces of rational curves, with an emphasis on applications to arithmetic questions. Classically, arithmetic is the study of rational or integral solutions of diophantine equations and geometry is the study of lines and conics. From the modern standpoint, arithmetic is the study of rational and integral points on algebraic varieties over nonclosed fields. A major insight of the 20th century was that arithmetic properties of an algebraic variety are tightly linked to the geometry of rational curves on the variety and how they vary in families. This collection of solicited survey and research papers is intended to serve as an introduction for graduate students and researchers interested in entering the field, and as a source of reference for experts working on related problems. Topics that will be addressed include: birational properties such as rationality, unirationality, and rational connectedness, existence of rational curves in prescribed homology classes, cones of rational curves on rationally connected and Calabi-Yau varieties, as well as related questions within the framework of the Minimal Model Program.

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