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Department of Mathematics
University of Oslo
Box 1053, Blindern, 0316 Oslo, Norway
Email: johnco@math.uio.no
Office: B621

CV

My research interests are in algebraic geometry.

Algebraic geometry group at UiO
Algebra/algebraic geometry seminar at UiO.

Events

Combinatorics and Hodge theory
18-22 June 2018, Sophus Lie Conference Center, Nordfjordeid, Norway.
Enumeration and Moduli: A conference in algebraic geometry on the occasion of Geir Ellingsrud's 70th birthday
December 6-8 2018, University of Oslo.
Geometry of Moduli
August 7, 2017 - Aug. 11, 2017, Lofoten, Norway.
Polar geometry: A conference celebrating the work of Ragni Piene on the occasion of her 70th birthday.
January 26-28, 2017, University of Oslo.
Nordfjordeid Summer School: Stability conditions on triangulated categories and geometric applications
June 13-17, 2016, Sophus Lie Conference Center, Nordfjordeid, Norway.

Teaching

MAT4215 Algebraic Geometry II (Spring 2018).

Students

Publications

Failure of the integral Hodge conjecture for threefolds of Kodaira dimension zero (with O. Benoist). arXiv (2018) PDF
A counterexample to the birational Torelli problem for Calabi-Yau 3-folds (with J. V. Rennemo). To appear in Journal of the London Mathematical Society (2018) PDF
Positivity of the diagonal (with B. Lehmann) PDF
Effective cones of cycles on blow-ups of projective space (with I. Coskun, J. Lesieutre). Algebra & Number Theory 10-9 (2016). PDF
Nef cycles on some hyperkahler fourfolds. PDF
Curves disjoint from a nef divisor (with J. Lesieutre). Michigan. Math. J. 65 (2016), 321--332. PDF
On subvarieties with ample normal bundle. Journal of the European Mathematical Society 18,(2016) 2459--2468 PDF
Quartic spectrahedra (with K. Ranestad, B. Sturmfels, C. Vinzant) Math. Prog. B (2015). PDF
Birational geometry of hypersurfaces in products of projective spaces. Mathematische Zeitschrift 280 (2015), 135-148 PDF
Ample subvarieties and q-ample divisors. Advances in Mathematics 229 (2012), 2868-2887. PDF
Algebraic boundaries of Hilbert's SOS cones (with G. Blekherman, J. Hauenstein, K. Ranestad and B. Sturmfels). Compositio Mathematica 148 (2012). PDF
Partially ample line bundles on toric varieties. (with N. Broomhead and A. Prendergast-Smith). Glasgow Math. J. 58 (2016) PDF
Components of the Hilbert scheme of space curves on low-degree smooth surfaces (with J. O. Kleppe). International Journal of Mathematics Vol. 26, (2015) PDF
The Cox ring of a K3 surface of Picard number two. Journal of Pure and Applied Algebra 217 (2013), 709-715. PDF
On the Cox Ring of P^2 Blown Up in Points on a Line. Mathematica Scandinavica 9, (2011), 21-31. PDF

Other

`Positivity of the diagonal'. Oberwolfach Report (2017) PDF
`Mori dream hypersurfaces'. Oberwolfach Report (2014) PDF
`Positivity of higher codimension cycles'. Summer school notes, Vlieland, September 2016. PDF