Work in progress

• Toric tangent developable. (with A. Dickenstein and R. Piene)
• Positivity of toric vactor bundles. (with G. Smith and K. Jabbusch)

Submitted papers

1. Mixed Discriminants.(with M.A. Cueto, E. Cattani, A. Dickenstein and B. Sturmfels) arXiv:1112.1012
   
2. Higher order duality and toric embeddings. arXiv:1111.4641  (with A. Dickenstein and R. Piene).
   
3. Polyhedral adjunction theory. ArXiv:1105.2415 (with B.Nill, C. Haase and A. Paffenholz).
4. Cell decomposition of almost real surfaces. PDF (with G.M. Besana, J.D. Hauenstein, A.J. Sommese, C.W. Wampler).

Accepted papers

1. The variety of bad zero-schemes. PDF (with G.M Besana and A. Lanteri). To appear in J. of Pure and Applied Algebra.
   
2. Recent developments and open problems in linear series.
   (with Th. Bauer, C. Bocci, Susan Cooper, M. Dumnicki, B. Harbourne, K. Jabbusch, A. Leopold Knutsen, A. Kuronya, R. Miranda, J. Roe, H. Schenck, T., Z. Teitler)  PDF ArXiv 2011
   to appear in "Contributions to Algebraic Geometry", Impanga Lecture Notes.
   
   

Published papers

1. The derived category of  fiber bundles.  PDF  
   (with L. Costa and R.M. Roig).
   Math. Research Letters, Vol. 18, (3), May 2011, pp. 425-432
2. Chern Numbers of Smooth Varieties via Homotopy Continuation and Intersection Theory. PDF
   (with D. Eklund, C. Petersen and A.J. Sommese)
   J. of Symbolic Computation 46 (2011) 23–33.
3. Algebraic C*-actions and the inverse kinematics of a general 6R manipulator. PDF
   (with D. Eklund, A. J. Sommese and C.W. Wampler),  Applied Mathematics and Computation
   Volume 216, Issue 9, 1 July 2010, Pages 2512-2524
   
4. Classifying polytopes via toric fibrations. PDF Arxiv 18/9/2008
   (with A. Dickenstein and R. Piene)
   Advances in Math, Vol. 222, 1, 10 September 2009, pp. 240-254
5. A primer on Seshadri constants. PDF Arxiv 04/10/2008
   (with Th. Bauer, B. Harbourne, M Kapustka, A. Knutsen, W. Sydek and T. Szemberg)
   Contemporary Mathematics, Vol. 496, 2009, pp. 33-70.
6. Projective Q-factorial toric varieties covered by lines. PDF
   C. Casagrande and S. Di Rocco
   Comm. in Contemporary Mathematics (CCM)10, 3 (June 2008)
7. Higher order bad loci. PDF
   G.M. Besana, S. Di Rocco and A. Lanteri
   J. of Pure and Applied Algebra, volume 211, 2 (November 2007), 414-427.
8. Projective duality of toric manifolds and defect polytopes. PDF
   S. Di Rocco
   Proc. LMS, volume 3 (93) 2006, n.1, pp 85-104.
9. Peculiar Loci of ample and spanned line bundles. PDF
   G.M. Besana, S. Di Rocco and A. Lanteri
   Manuscripta Mathematica, 112 (2003) 197-219.
10. Chern numbers of ample vector bundles on toric surfaces. PDF
    S. Di Rocco and A. J. Sommese
    Trans. Amer. Math. Soc. 356 (2004), no. 2, 587--598.
11. Polarized surfaces whose adjoint bundles are not spanned.
    G.M. Besana and S. Di Rocco
    J.Math.Soc.Japan, 54 (2002).
12. Line bundles for which a projectivized jet bundle is a product. PDF
    S. Di Rocco and A. J. Sommese
    Proc. of A.M.S. 129 (2001), no. 6, 1659--1663.
13. Cyclic coverings and higher order embeddings of algebraic varieties. PDF
    Th. Bauer, S. Di Rocco and T. Szemberg
    Transactions of the A.M.S., 356 (2004), 587-598.
14. Generation of jets on K3 surfaces. PDF
    Th. Bauer, S. Di Rocco and T. Szemberg
    Proc. of the London Mathematical Society, 93, 01 (Jul 2006) 85-104.
15. On surfaces in P^6 with no trisecant lines. PDF
    S. Di Rocco and K. Ranestad
    Arkiv för Matematik, 38(2), 2000.
16. On generation of jets for vector bundles.
    M. Beltrametti, S. Di Rocco and A. J. Sommese
    Rev. Mat. Complut.,12, 27-45 (1999).
17. Generation of k-jets on toric varieties. PDF
    S. Di Rocco
    Math. Z., 231, 169-188, (1999).
18. On higher order embeddings and n-connectedness.
    M. Beltrametti, S. Di Rocco an A. Lanteri
    Mat. Nachr 201 (1999), 37-5.
19. On generation of jets for vector bundles.
    M. Beltrametti, S. Di Rocco and A. J. Sommese
    Rev. Mat. Complut. 12 (1999), no. 1, 27--45.
20. On Higher Order Embeddings of Fano Threefolds by the anticanonical linear system.
    M. Beltrametti, S. Di Rocco and A. J. Sommese
    Math. Nachr. 201 (1999), 37--51.
21. k-very Ample Line Bundles on Del Pezzo Surfaces. PDF
    S. Di Rocco
    Mat. Nachr., 179 (1996), 47--56.
22. Projective Surfaces with k-very Ample Line bundles of genus <3k+2. PDF
    S. Di Rocco
    Manuscripta Mathematica, 91, 1 (1996), 35--59.