Positivity and geometry of higher codimension subvarieties
About the project
This is a project in algebraic geometry, a subject whose overlying goal is to classify and study algebraic varieties.
The project revolves around several central questions related to algebraic cycles, birational geometry, and Hodge theory. The main theme of the project is to explore how geometric properties of an algebraic variety are reflected in its special subvarieties. One example is given by socalled `positive subvarieties', e.g., subvarieties having nonnegative intersection numbers with all other subvarieties.
Outcomes

On deformations of quintic and septic hypersurfaces (with S. Schreieder) (2018)
 Remarks on the positivity of the cotangent bundle of a K3 surface (with F. Gounelas) (2018)
 Curve classes on irreducible holomorphic symplectic varieties (with G. Mongardi) (2018)
 Failure of the integral Hodge conjecture for threefolds of Kodaira dimension zero (with O. Benoist). To appear in Commentarii Mathematici Helvetici (2018)
 A counterexample to the birational Torelli problem for CalabiYau 3folds (with J. V. Rennemo). Journal of the London Mathematical Society 97 (2018), 427440
 Positivity of the diagonal (with B. Lehmann). Advances in Mathematics 335 (2018), 664695.
 Effective cones of cycles on blowups of projective space (with I. Coskun, J. Lesieutre). Algebra & Number Theory 109 (2016).
 Nef cycles on some hyperkahler fourfolds. (2016)
Financing
Research Council of Norway, Independent projects  Young research talent. Project number 250104, total budget 9,2 mill NOK.