Department of
Mathematics

University of Oslo

Box 1053, Blindern, 0316 Oslo, Norway

Email: johnco@math.uio.no

Office: B621

My research interests are in algebraic geometry.

18-22 June 2018, Sophus Lie Conference Center, Nordfjordeid, Norway.

December 6-8 2018, University of Oslo.

August 7, 2017 - Aug. 11, 2017, Lofoten, Norway.

January 26-28, 2017, University of Oslo.

June 13-17, 2016, Sophus Lie Conference Center, Nordfjordeid, Norway.

**MAT4215
Algebraic Geometry II** (Spring 2018).

Failure of the integral Hodge conjecture for threefolds of Kodaira dimension zero (with O. Benoist). To appear in *Commentarii Mathematici Helvetici* (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

`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