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Dive into the research topics where Rajesh S. Kulkarni is active.

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Featured researches published by Rajesh S. Kulkarni.


Journal of Algebra | 2013

THE GEOMETRY OF ULRICH BUNDLES ON DEL PEZZO SURFACES

Emre Coskun; Rajesh S. Kulkarni; Yusuf Mustopa

Abstract Given a smooth del Pezzo surface X d ⊆ P d of degree d, we isolate the essential geometric obstruction to a vector bundle on X d being an Ulrich bundle by showing that an irreducible curve D of degree dr on X d represents the first Chern class of a rank-r Ulrich bundle on X d if and only if the kernel bundle of the general smooth element of | D | admits a generalized theta-divisor. Moreover, we show that any smooth arithmetically Gorenstein surface whose Ulrich bundles admit such a characterization is necessarily del Pezzo. This result is applied to produce new examples of complete intersection curves with semistable kernel bundle, and also combined with work of Farkas, Mustaţǎ and Popa to relate the existence of Ulrich bundles on X d to the Minimal Resolution Conjecture for curves lying on X d . In particular, we show that a smooth irreducible curve D of degree 3r lying on a smooth cubic surface X 3 represents the first Chern class of an Ulrich bundle on X 3 if and only if the Minimal Resolution Conjecture holds for the general smooth element of | D | .


Advances in Mathematics | 2003

Del Pezzo orders on projective surfaces

Daniel Chan; Rajesh S. Kulkarni

Abstract In this paper, we generalise the notion of del Pezzo surfaces to orders on surfaces. We show that these del Pezzo orders have del Pezzo centre if the centre is normal Gorenstein and the order has finite representation type. We proceed to classify these del Pezzo orders. The main result is that if the centre is not P 1 × P 1 or the quadric cone, then these del Pezzo orders can be obtained from del Pezzo orders on P 2 . Finally, we classify del Pezzo orders on P 2 , P 1 × P 1 and the quadric cone.


Journal of The London Mathematical Society-second Series | 2005

Numerically Calabi–Yau Orders on Surfaces

Daniel Chan; Rajesh S. Kulkarni

The work in this paper is part of an ongoing program to classify maximal orders on surfaces via their ramification data. Del Pezzo orders and ruled orders have already been classified by the authors and others. In this paper, we classify numerically Calabi–Yau orders which are the noncommutative analogues of minimal surfaces of Kodaira dimension zero.


Transactions of the American Mathematical Society | 2003

On the Clifford algebra of a binary form

Rajesh S. Kulkarni

The Clifford algebra Cj of a binary form f of degree d is the k-algebra k{x,y}/I, where I is the ideal generated by {(ax + βy) d - f(α, β) | α, β E k}. C f has a natural homomorphic image A f that is a rank d 2 Azumaya algebra over its center. We prove that the center is isomorphic to the coordinate ring of the complement of an explicit Θ-divisor in Pic d+g-1 C/κ, where C is the curve (w d - f(u, v)) and g is the genus of C.


Proceedings of the American Mathematical Society | 2008

Down-up algebras at roots of unity

Rajesh S. Kulkarni

In this note, we show that down-up algebras at roots of unity are maximal orders over their centers.


Mathematische Zeitschrift | 2017

Vector bundles whose restriction to a linear section is Ulrich

Rajesh S. Kulkarni; Yusuf Mustopa; Ian Shipman

An Ulrich sheaf on an n-dimensional projective variety


Journal of Algebra | 2001

Down–Up Algebras and Their Representations

Rajesh S. Kulkarni


Documenta Mathematica | 2012

Pfaffian quartic surfaces and representations of Clifford algebras

Emre Coskun; Rajesh S. Kulkarni; Yusuf Mustopa

X \subseteq \mathbb {P}^{N}


arXiv: Rings and Algebras | 2011

On representations of Clifford algebras of ternary cubic forms

Emre Coskun; Rajesh S. Kulkarni; Yusuf Mustopa


Journal of Algebra | 1999

Irreducible Representations of Witten's Deformations ofU(sl2)

Rajesh S. Kulkarni

X⊆PN is an initialized ACM sheaf which has the maximum possible number of global sections. Using a construction based on the representation theory of Roby–Clifford algebras, we prove that every normal ACM variety admits a reflexive sheaf whose restriction to a general 1-dimensional linear section is Ulrich; we call such sheaves

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Emre Coskun

Middle East Technical University

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Daniel Chan

University of New South Wales

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Kenneth Chan

University of Washington

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Markus Banagl

University of Cincinnati

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Max Lieblich

University of Washington

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Boris Lerner

University of New South Wales

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Colin Ingalls

University of New Brunswick

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