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You searched for +publisher:"University of Kansas" +contributor:("Purnaprajna, Bangere"). Showing records 1 – 3 of 3 total matches.

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University of Kansas

1. Rajaguru, Biswajit. Projective normality for some families of surfaces of general type.

Degree: PhD, Mathematics, 2017, University of Kansas

In this thesis, we present the author's joint research with Lei Song, published in . We show this: Suppose X is a minimal surface, which is a ramified double covering f:X- S, of a rational surface S, with dim |-KS|= 1. And suppose L is a divisor on S, such that L.L= 7 and L. C= 3 for any curve C on S. Then KX+f*L is base-point free and the natural map Symr(H0(KX+f*L))- H0(r(KX+f*L)), is surjective for all r=1. In particular this implies, when S is also smooth and L is an ample line bundle on S, that KX+nf*L embeds X as a projectively normal variety for all n = 3. Advisors/Committee Members: Purnaprajna, Bangere (advisor), Purnaprajna, Bangere (cmtemember), Mandal, Satyagopal (cmtemember), Lang, Jeffrey (cmtemember), Greenberg, Marc (cmtemember), Jiang, Yunfeng (cmtemember).

Subjects/Keywords: Mathematics; anticanonical rational surfaces; mukai's conjecture; projective normality

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APA (6th Edition):

Rajaguru, B. (2017). Projective normality for some families of surfaces of general type. (Doctoral Dissertation). University of Kansas. Retrieved from http://hdl.handle.net/1808/26022

Chicago Manual of Style (16th Edition):

Rajaguru, Biswajit. “Projective normality for some families of surfaces of general type.” 2017. Doctoral Dissertation, University of Kansas. Accessed July 02, 2020. http://hdl.handle.net/1808/26022.

MLA Handbook (7th Edition):

Rajaguru, Biswajit. “Projective normality for some families of surfaces of general type.” 2017. Web. 02 Jul 2020.

Vancouver:

Rajaguru B. Projective normality for some families of surfaces of general type. [Internet] [Doctoral dissertation]. University of Kansas; 2017. [cited 2020 Jul 02]. Available from: http://hdl.handle.net/1808/26022.

Council of Science Editors:

Rajaguru B. Projective normality for some families of surfaces of general type. [Doctoral Dissertation]. University of Kansas; 2017. Available from: http://hdl.handle.net/1808/26022


University of Kansas

2. Alkarni, Shalan. Three Dimensional Jacobian Derivations And Divisor Class Groups.

Degree: PhD, Mathematics, 2016, University of Kansas

In this thesis, we use P. Samuel's purely inseparable descent methods to investigate the divisor class groups of the intersections of pairs of hypersurfaces of the form w1p=f, w2p=g in affine 5-space with f, g in A=k[x,y,z]; k is an algebraically closed field of characteristic p 0. This corresponds to studying the divisor class group of the kernels of three dimensional Jacobian derivations on A that are regular in codimension one. Our computations focus primarily on pairs where f, g are quadratic forms. We find results concerning the order and the type of these groups. We show that the divisor class group is a direct sum of up to three copies of ℤp, is never trivial, and is generated by those hyperplane sections whose forms are factors of linear combinations of f and g. Advisors/Committee Members: Lang, Jeffrey (advisor), Mandal, Satyagopal (cmtemember), Purnaprajna, Bangere (cmtemember), Jiang, Yunfeng (cmtemember), Brinton, Jacquelene (cmtemember).

Subjects/Keywords: Mathematics; Algebra; Algebraic Geometry; Class Groups; Commutative Algebra; Divisors; Group of Logarithmic Derivatives

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APA (6th Edition):

Alkarni, S. (2016). Three Dimensional Jacobian Derivations And Divisor Class Groups. (Doctoral Dissertation). University of Kansas. Retrieved from http://hdl.handle.net/1808/21802

Chicago Manual of Style (16th Edition):

Alkarni, Shalan. “Three Dimensional Jacobian Derivations And Divisor Class Groups.” 2016. Doctoral Dissertation, University of Kansas. Accessed July 02, 2020. http://hdl.handle.net/1808/21802.

MLA Handbook (7th Edition):

Alkarni, Shalan. “Three Dimensional Jacobian Derivations And Divisor Class Groups.” 2016. Web. 02 Jul 2020.

Vancouver:

Alkarni S. Three Dimensional Jacobian Derivations And Divisor Class Groups. [Internet] [Doctoral dissertation]. University of Kansas; 2016. [cited 2020 Jul 02]. Available from: http://hdl.handle.net/1808/21802.

Council of Science Editors:

Alkarni S. Three Dimensional Jacobian Derivations And Divisor Class Groups. [Doctoral Dissertation]. University of Kansas; 2016. Available from: http://hdl.handle.net/1808/21802

3. Stone, Branden. Super-Stretched and Countable Cohen-Macaulay Type.

Degree: PhD, Mathematics, 2012, University of Kansas

This dissertation defines what it means for a Cohen-Macaulay ring to to be super-stretched. In particular, a super-stretched Cohen-Macaulay ring of positive dimension has h-vector (1), (1,n), or (1,n,1). It is shown that Cohen-Macaulay rings of graded countable Cohen-Macaulay type are super-stretched. Further, one dimensional standard graded Gorenstein rings of graded countable type are shown to be hypersurfaces; this result is not known in higher dimensions. In Chapter 1, some background material is given along with some preliminary definitions. This chapter defines what it means to be stretched and super-stretched. The chapter ends by showing a couple of scenarios when these two notions coincide. Chapter 2 deals with super-stretched rings that are standard graded. We begin the chapter by exploring the graded category and defining what it means to be graded countable Cohen-Macaulay type. Equivalent characterizations of super-stretched are discovered and it is shown that rings of graded countable Cohen-Macaulay type are super-stretched. The chapter ends by analyzing standard graded rings that are super-stretched with minimal multiplicity. In Chapter 3, we examine what it means for a local ring to be super-stretched. Finally, Chapter 4 uses the previous results to give a partial answer to the following question: Let R be a standard graded Cohen-Macaulay ring of graded countable Cohen-Macaulay representation type, and assume that R has an isolated singularity. Is R then necessarily of graded finite Cohen-Macaulay representation type? In particular, it is shown there is a positive answer when the ring is not Gorenstein. Throughout the chapter, many different cases of graded countable Cohen-Macaulay type are classified. Further, the Gorenstein case is studied is shown to be helpful in giving support to the following folklore conjecture: a Gorenstein ring of countable Cohen-Macaulay representation type is a hypersurface. It is shown that the conjecture holds for one dimensional standard graded Cohen-Macaulay rings of graded countable Cohen-Macaulay type. Advisors/Committee Members: Huneke, Craig (advisor), Katz, Daniel (cmtemember), Dao, Hailong (cmtemember), Purnaprajna, Bangere (cmtemember), Agah, Arvin (cmtemember).

Subjects/Keywords: Mathematics; Countable type; Maximal cohen macaulay; Super-stretched

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APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6th Edition):

Stone, B. (2012). Super-Stretched and Countable Cohen-Macaulay Type. (Doctoral Dissertation). University of Kansas. Retrieved from http://hdl.handle.net/1808/10808

Chicago Manual of Style (16th Edition):

Stone, Branden. “Super-Stretched and Countable Cohen-Macaulay Type.” 2012. Doctoral Dissertation, University of Kansas. Accessed July 02, 2020. http://hdl.handle.net/1808/10808.

MLA Handbook (7th Edition):

Stone, Branden. “Super-Stretched and Countable Cohen-Macaulay Type.” 2012. Web. 02 Jul 2020.

Vancouver:

Stone B. Super-Stretched and Countable Cohen-Macaulay Type. [Internet] [Doctoral dissertation]. University of Kansas; 2012. [cited 2020 Jul 02]. Available from: http://hdl.handle.net/1808/10808.

Council of Science Editors:

Stone B. Super-Stretched and Countable Cohen-Macaulay Type. [Doctoral Dissertation]. University of Kansas; 2012. Available from: http://hdl.handle.net/1808/10808

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