Research

This page describes my research interests.
My research interests are in algebraic geometry. I am one of the organisers of the COW seminar. I also used to act as deputy coordinator of the British (Warwick) node of the European algebraic geometry network EAGER. It no longer exists as a network, but the mailing list is still active.

Much of my recent work has been on locally symmetric varieties and their compactifications, especially using the existence of special modular forms to extract geometric information, and examining the combinatorics that go on in the boundary. Mostly in the past I have been concerned with moduli of abelian varieties and thus with the symplectic group, but more recently I have spent more effort on orthogonal groups and especially on K3 surfaces and hyperkähler manifolds.

My research students

  1. Alfio Marini graduated in 2002.
    Alfio Marini's thesis as Postscript or PDF.
  2. Al Kasprzyk graduated in 2006.
    Al Kasprzyk's thesis as Postscript or PDF.
  3. Marco Lo Giudice graduated in 2006 with a Ph.D. at the Università di Milano.
    Marco Lo Giudice's thesis as Postscript or PDF.
  4. Nathan Broomhead graduated in 2009. He was supervised by Alastair King and me jointly.
    Nathan Broomhead's thesis as Postscript or PDF.
  5. Lisema Rammea graduated in 2009.
    Lisema Rammea's thesis as Postscript or PDF.
  6. Pawel Borowka started in September 2008.
  7. Atika Ahmed started in February 2010.
  8. Acyr Locatelli is supervised by James Davenport and me jointly. He started in October 2011.
  9. Matthew Dawes started in October 2011.

Here are some recent papers of mine:

  1. Moduli of K3 surfaces and irreducible symplectic manifolds [ps] [pdf]
    V. Gritsenko, K. Hulek and G.K. Sankaran. arXiv:1012.4155 To appear in Handbook of Moduli.

  2. On some lattice computations related to moduli problems [ps] [pdf]
    A. Peterson and G.K. Sankaran, with an appendix by V. Gritsenko. Rend. Sem. Mat. Univ. Pol. Torino 68 No. 3 (2010), 289-304.
    There is a supplement containing the computer programs used in this paper.

  3. Moduli spaces of polarised symplectic O'Grady varieties and Borcherds products [ps] [pdf]
    V. Gritsenko, K. Hulek and G.K. Sankaran. J. Differential Geometry 88 No. 1 (2011), 61-85

  4. Smooth rationally connected threefolds contain all smooth curves [ps] [pdf]
    G.K. Sankaran. In: W. Ebeling, K. Hulek & K. Smoczyk (Eds.), Complex and Differential Geometry, Springer Proceedings in Mathematics 8 (2011), 393-402.

  5. Boundedness for surfaces in weighted projective 4-spaces [ps] [pdf]
    L.V. Rammea and G.K. Sankaran. Proc. Amer. Math. Soc. 139 (2011), 3393-3403.

  6. Abelianisation of orthogonal groups and the fundamental group of modular varieties [ps] [pdf]
    V. Gritsenko, K. Hulek and G.K. Sankaran. J. Algebra 322 (2009), 463-478.

  7. Moduli spaces of irreducible symplectic manifolds [ps] [pdf]
    V. Gritsenko, K. Hulek and G.K. Sankaran. Compositio Math. 146 (2010) 404-434.

  8. The moduli space of étale double covers of genus 5 curves is unirational [ps] [pdf]
    E. Izadi, M. Lo Giudice and G.K. Sankaran. Pacific J. Math. 239 (2009), 39-52.

  9. Numerical obstructions to abelian surfaces in toric Fano 4-folds [ps] [pdf]
    G.K. Sankaran. Kodai Math. J. 31 (2008), 1-20.
    (This, among other things, corrects the error in Abelian surfaces in toric 4-folds, below.)

  10. Hirzebruch-Mumford proportionality and locally symmetric varieties of orthogonal type [ps] [pdf]
    V. Gritsenko, K. Hulek and G.K. Sankaran. Documenta Math. 13 (2008), 1-19.

  11. The Kodaira dimension of the moduli of K3 surfaces [ps] [pdf]
    V. Gritsenko, K. Hulek and G.K. Sankaran. Invent. Math. 167 (2007), 519-567.
    The original publication is available at www.springerlink.com.

  12. The Hirzebruch-Mumford volume for the orthogonal group and applications [ps] [pdf]
    V. Gritsenko, K. Hulek and G.K. Sankaran. Documenta Math. 12 (2007), 215-241.

  13. The nef cone of toroidal compactifications of A4 [ps] [pdf]
    K. Hulek and G.K. Sankaran. Proc. London Math. Soc. 88 (2004), 659-704.

  14. Abelian surfaces with odd bilevel structure [ps] [pdf]
    G.K. Sankaran. In: M. Reid, A. Skorobogatov (Eds.), Number theory and algebraic geometry, London Math. Soc. Lecture Note Series, 303 (2003), 279-300.

  15. The moduli space of bilevel-6 abelian surfaces [ps] [pdf]
    G.K. Sankaran and J. Spandaw. Nagoya Math. J. 168 (2002), 113-125.

  16. Das Titsgebäude von Siegelschen Modulgruppen vom Geschlecht 2 [ps] [pdf]
    M. Friedland and G.K. Sankaran. Abh. Math. Sem. Univ. Hamburg 71 (2001), 49-68.
    (In German; but there is a supplement with an English summary [ps] [pdf] and some pictures)

  17. Algebraic construction of normalized coprime factors for delay systems [ps] [pdf]
    J.R. Partington and G.K. Sankaran. Math. Control Signals Systems 15 (2002), 1-12.
    (I know nothing about this subject)

  18. The geometry of Siegel modular varieties [ps] [pdf]
    K. Hulek and G.K. Sankaran. In: S. Mori, Y. Miyaoka (Eds.), Higher Dimensional Birational Geometry, Advanced Studies in Pure Mathematics 35 (2002), 89-156.
    (A survey article)

  19. Abelian surfaces in toric 4-folds [ps] [pdf]
    G.K. Sankaran. Math. Ann. 313 (1999), 409-427.
    Warning: this paper contains a significant error. Here is a correction. [ps] [pdf]

  20. Degenerations of (1,3) abelian surfaces and Kummer surfaces [ps] [pdf]
    K. Hulek, I. Nieto and G.K. Sankaran. In: P. Pragacz, M. Szurek, J. Wisniewski (Eds.), Algebraic Geometry: Hirzebruch 70, AMS Contemporary Mathematics 241 (1999), 177-192.

  21. Heisenberg-invariant Kummer surfaces [ps] [pdf]
    K. Hulek, I. Nieto and G.K. Sankaran. Proc. Edin. Math. Soc. 43 (2000), 425-439.

Other pages of mine:

Teaching  - -  Personal  - -  General

Last modified 23rd September, 2011.
Maintained by: G.K.Sankaran@bath.ac.uk