Rajesh S. Kulkarni
Michigan State University
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Featured researches published by Rajesh S. Kulkarni.
Journal of Algebra | 2013
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
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
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
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
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
Rajesh S. Kulkarni; Yusuf Mustopa; Ian Shipman
An Ulrich sheaf on an n-dimensional projective variety
Journal of Algebra | 2001
Rajesh S. Kulkarni
Documenta Mathematica | 2012
Emre Coskun; Rajesh S. Kulkarni; Yusuf Mustopa
X \subseteq \mathbb {P}^{N}
arXiv: Rings and Algebras | 2011
Emre Coskun; Rajesh S. Kulkarni; Yusuf Mustopa
Journal of Algebra | 1999
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