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publications

Effective cycles on blow-ups of Grassmannians

Published in Journal of Pure and Applied Algebra, 2018

In this paper we study the pseudoeffective cones of blow-ups of Grassmannians at sets of points. For small numbers of points, the cones are often spanned by proper transforms of Schubert classes. In some special cases, we provide sharp bounds for when the Schubert classes fail to span and we describe the resulting geometry.

Recommended citation: J. Kopper. Effective cycles on blow-ups of Grassmannians. Journal of Pure and Applied Algebra, 222 no. 4 (2018), 846--86769.

The nef cone of the Hilbert scheme of points on rational elliptic surfaces and the cone conjecture

Published in Canadian Mathematical Bulletin, 2020

We compute the nef cone of the Hilbert scheme of points on a general rational elliptic surface. As a consequence of our computation, we show that the Morrison-Kawamata cone conjecture holds for these nef cones.

Recommended citation: J. Kopper. The nef cone of the Hilbert scheme of points on rational elliptic surfaces and the cone conjecture. Canadian Mathematical Bulletin 64 no. 1 (2020), 216--227.

Stability conditions for restrictions of vector bundles on projective surfaces

Published in Michigan Mathematical Journal, 2020

Using Bridgeland stability conditions, we give sufficient criteria for a stable vector bundle on a smooth complex projective surface to remain stable when restricted to a curve. We give a stronger criterion when the vector bundle is a general vector bundle on the plane. As an application, we compute the cohomology of such bundles for curves that lie in the plane or on Hirzebruch surfaces.

Recommended citation: J. Kopper. Stability conditions for restrictions of vector bundles on projective surfaces. Michigan Mathematical Journal 69 no. 4 (2020), 711--732..

The cohomology of general tensor products on the plane

Published in Selecta Mathematica, 2021

We compute the cohomology of general tensor products of stable bundles on the projective plane.

Recommended citation: I. Coskun, J. Huizenga, and J. Kopper. The cohomology of general tensor products on the plane. Selecta Mathematica 27 no. 5 (2021), article number 94.

Ample stable vector bundles on rational surfaces

Published in Communications in Algebra, 2022

We study sufficient and necessary conditions for stable vector bundles on the plane to be ample. Joint work with Jack Huizenga.

Recommended citation: J. Huizenga, and J. Kopper. Ample stable vector bundles on rational surfaces. Communications in Algebra (2022), to appear.

Non–globally generated bundles on curves

Published in International Mathematics Research Notices, 2022

We study the locus of stable vector bundles on smooth curves that fail to be globally generated. We compute the dimension of this locus and study its irreducibility. Joint work with Sayanta Mandal.

Recommended citation: J. Kopper and S. Mandal. Non-globally generated bundles on curves. International Mathematics Research Notices (2022), to appear.

Disconnected moduli spaces of stable bundles on surfaces

Published in Bulletin of the London Mathematical Society, 2022

We construct moduli spaces of stable bundles on surfaces with arbitrarily many connected components. Joint work with Izzet Coskun and Jack Huizenga.

Recommended citation: I. Coskun, J. Huizenga, and J. Kopper. Disconnected moduli spaces of stable bundles on surfaces. Bull. Lond. Math. Soc. (2022), to appear.

teaching

Teaching experience 1

Undergraduate course, University 1, Department, 2014

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Teaching experience 2

Workshop, University 1, Department, 2015