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Author : Atanas Atanasov
Release : 2018
Genre : Curves, Algebraic
Kind : eBook
Book Rating : 513/5 ( reviews)
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 2018. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Atanas Atanasov
Release : 2019-02-21
Genre : Curves, Algebraic
Kind : eBook
Book Rating : 89X/5 ( reviews)
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.
Author : Atanas Valeryev Atanasov
Release : 2015
Genre :
Kind : eBook
Book Rating : /5 ( reviews)
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.
Author : Dominic Joyce
Release : 2019-09-05
Genre :
Kind : eBook
Book Rating : 450/5 ( reviews)
Book Synopsis Algebraic Geometry over C∞-Rings by : Dominic Joyce
Download or read book Algebraic Geometry over C∞-Rings written by Dominic Joyce. This book was released on 2019-09-05. Available in PDF, EPUB and Kindle. Book excerpt: If X is a manifold then the R-algebra C∞(X) of smooth functions c:X→R is a C∞-ring. That is, for each smooth function f:Rn→R there is an n-fold operation Φf:C∞(X)n→C∞(X) acting by Φf:(c1,…,cn)↦f(c1,…,cn), and these operations Φf satisfy many natural identities. Thus, C∞(X) actually has a far richer structure than the obvious R-algebra structure. The author explains the foundations of a version of algebraic geometry in which rings or algebras are replaced by C∞-rings. As schemes are the basic objects in algebraic geometry, the new basic objects are C∞-schemes, a category of geometric objects which generalize manifolds and whose morphisms generalize smooth maps. The author also studies quasicoherent sheaves on C∞-schemes, and C∞-stacks, in particular Deligne-Mumford C∞-stacks, a 2-category of geometric objects generalizing orbifolds. Many of these ideas are not new: C∞-rings and C∞ -schemes have long been part of synthetic differential geometry. But the author develops them in new directions. In earlier publications, the author used these tools to define d-manifolds and d-orbifolds, “derived” versions of manifolds and orbifolds related to Spivak's “derived manifolds”.
Author : Ines Kath
Release : 2020-02-13
Genre : Education
Kind : eBook
Book Rating : 039/5 ( reviews)
Book Synopsis Compact Quotients of Cahen-Wallach Spaces by : Ines Kath
Download or read book Compact Quotients of Cahen-Wallach Spaces written by Ines Kath. This book was released on 2020-02-13. Available in PDF, EPUB and Kindle. Book excerpt: Indecomposable symmetric Lorentzian manifolds of non-constant curvature are called Cahen-Wallach spaces. Their isometry classes are described by continuous families of real parameters. The authors derive necessary and sufficient conditions for the existence of compact quotients of Cahen-Wallach spaces in terms of these parameters.
