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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 so-called `positive subvarieties', e.g., subvarieties having non-negative intersection numbers with all other subvarieties.

Outcomes

  1. A pencil of Enriques surfaces with non-algebraic integral Hodge classes (with F. Suzuki) (2019)

  2. On deformations of quintic and septic hypersurfaces (with S. Schreieder) (2018)

  3. Remarks on the positivity of the cotangent bundle of a K3 surface (with F. Gounelas) (2018)
  4. Curve classes on irreducible holomorphic symplectic varieties (with G. Mongardi) (2018)
  5. Failure of the integral Hodge conjecture for threefolds of Kodaira dimension zero (with O. Benoist). To appear in Commentarii Mathematici Helvetici (2018)
  6. A counterexample to the birational Torelli problem for Calabi-Yau 3-folds (with J. V. Rennemo). Journal of the London Mathematical Society 97 (2018), 427-440
  7. Positivity of the diagonal (with B. Lehmann). Advances in Mathematics 335 (2018), 664-695.
  8. Effective cones of cycles on blow-ups of projective space (with I. Coskun, J. Lesieutre). Algebra & Number Theory 10-9 (2016).
  9. Nef cycles on some hyperkahler fourfolds. (2016)
  10. Huybrechts, D.; Rennemo, J. V. Hochschild Cohomology versus the Jacobian Ring and the Torelli Theorem for Cubic Fourfolds. Algebr. Geom. 20196 (1), 76–99.
  11. Automorphisms of Hilbert schemes of points on surfaces (P. Belmans, G. Oberdieck, J. V. Rennemo)
  12. A proof of the Donaldson-Thomas crepant resolution conjecture (S. Beentjes, J. Calabrese, J.V. Rennemo)
  13. Some ways to reconstruct a sheaf from its tautological image on a Hilbert scheme of points A. Krug, J. V. Rennemo
  14. Singularities of Restriction Varieties in OG(k,n): S. Adalı.

Financing

Research Council of Norway, Independent projects - Young research talent. Project number 250104, total budget 9,2 mill NOK.

Tags: Mathematics, algebraic geometry
Published Mar. 2, 2018 6:37 PM - Last modified Sep. 15, 2019 5:26 PM