Department of Mathematics
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Instanton Bundles on the Blowup of the Projective 3-Space at a Point
Coşkun, Emre; Genç, Özhan; Malaspina, Francesco; Casnati, Gianfranco (2021-10-01)
We propose a general definition of mathematical instanton bundle with given charge on any Fano threefold extending the classical definitions on P3 and on Fano threefold with cyclic Picard group. Then we deal with the cas...
Coşkun, Emre; Genc, Ozhan (American Mathematical Society (AMS), 2017-11-01)
We prove that every Ulrich bundle on the Veronese surface has a resolution in terms of twists of the trivial bundle over P-2. Using this classification, we prove existence results for stable Ulrich bundles over P-k with re...
A survey of Ulrich bundles
Coşkun, Emre (2017-06-12)
The purpose of this article is to serve as an introduction to Ulrich bundles for interested readers. We discuss the origins of the study of Ulrich bundles, their elementary properties, and we give an exposition of the kn...
The period-index problem of the canonical gerbe of symplectic and orthogonal bundles
BİSWAS, Indranil; Coşkun, Emre; DHİLLON, Ajneet (2016-01-15)
We consider regularly stable parabolic symplectic and orthogonal bundles over an irreducible smooth projective curve over an algebraically closed field of characteristic zero. The morphism from the moduli stack of such bun...
Ulrich bundles on quartic surfaces with Picard number 1
Coşkun, Emre (Elsevier BV, 2013-03-01)
In this note, we prove that there exist stable Ulrich bundles of every even rank on a smooth quartic surface X subset of P-3 with Picard number 1. (C) 2013 Academie des sciences. Published by Elsevier Masson SAS. All right...
The geometry of Ulrich bundles on del Pezzo surfaces
Coşkun, Emre; Kulkarni, Rajesh S.; MUSTOPA, Yusuf (2013-02-01)
Given a smooth del Pezzo surface X-d subset of 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 rep...
Coşkun, Emre; Kulkarni, Rajesh S.; Mustopa, Yusuf (2012-01-01)
Given a general ternary form f = f(x(1), x(2), x(3)) of degree 4 over an algebraically closed field of characteristic zero, we use the geometry of K3 surfaces and van den Bergh's correspondence between representations of t...
The Fine Moduli Space of Representations of Clifford Algebras
Coşkun, Emre (Oxford University Press (OUP), 2011-01-01)
Given a fixed binary form f(u,v) of degree d over a field k, the associated Clifford algebra is the k-algebra C(f)=k{u,v}/I, where I is the two-sided ideal generated by elements of the form (alpha u+beta v)(d)-f(alpha,beta...
On representations of Clifford algebras of Ternary cubic forms
Coşkun, Emre; Kulkarni, Rajesh S.; Mustopa, Yusuf (2010-08-14)
In this article, we provide an overview of a one-to-one correspondence between representations of the generalized Clifford algebra C-f of a ternary cubic form f and certain vector bundles (called Ulrich bundles) on a cubic...
On Nori s obstruction to universal bundles
Coşkun, Emre; Dhillon, Ajneet; Lemire, Nicole (2010-01-01)
Let G be SLn, Sp2n or SO2n. We consider the moduli space M of semistable principal G-bundles over a curve X. Our main result is that if U is a Zariski open subset of M then there is no universal bundle on U × X.
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