Research
This page describes my research interests.
My research interests are in algebraic geometry.
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. Originally I was
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
 Alfio Marini graduated in 2002.
Alfio Marini's
thesis as Postscript or
PDF.
 Al Kasprzyk
graduated in 2006.
Al Kasprzyk's thesis
as Postscript
or PDF.

Marco Lo Giudice
graduated in 2006 with a Ph.D. at the Università di Milano.
Marco Lo Giudice's thesis as Postscript or
PDF.

Nathan Broomhead
graduated in 2009. He was supervised by
Alastair King and me
jointly.
Nathan Broomhead's thesis as Postscript or
PDF.

Lisema Rammea
graduated in 2009.
Lisema Rammea's thesis as Postscript or
PDF.

Paweł Borówka graduated in 2012.
Paweł Borówka's thesis as Postscript or
PDF.

Atika Ahmed started in February 2010 and later withdrew for personal reasons.

Acyr Locatelli graduated in 2015. He was supervised by
James Davenport
and me jointly.
Acyr Locatelli's thesis as Postscript or
PDF.

Matthew Dawes graduated in 2015.
Matthew Dawes' thesis as Postscript or
PDF.

Claudio Onorati graduated 2018.
Claudio Onorati's thesis as
PDF.

Akshar Nair started in 2017. He is supervised by James Davenport and me jointly.
Here are some recent papers of mine:

Fast Matrix Operations in Computer Algebra
[pdf]
Z. Tonks, J.H. Davenport and G.K. Sankaran.

Regular Cylindrical Algebraic Decomposition [pdf]
J.H. Davenport, A.F. Locatelli and G.K. Sankaran.

Weighted CastelnuovoMumford regularity and weighted global generation [ps] [pdf]
F. Malaspina and G.K. Sankaran. J. Algebra Appl. 18 No. 2 (2019), 1950028

Genus 4 curves on abelian surfaces [ps] [pdf]
P. Borówka and G.K. Sankaran. Proc. Amer. Math. Soc. 145 No. 12 (2017), 5023–5034

Fundamental groups of toroidal compactifications [ps] [pdf]
A.K. Kasparian and G.K. Sankaran. Asian J. Math. 22 No. 5 (2018), 941954.

Moduli of K3 surfaces and irreducible symplectic manifolds [ps] [pdf]
V. Gritsenko, K. Hulek and G.K. Sankaran.
In: G. Farkas & I. Morrison (Eds.), Handbook of Moduli, Vol I, Adv. Lect. Math. (ALM) 24 Int. Press, Somerville, MA (2013), 459526

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), 289304.
There is a supplement
containing the computer programs used in this paper.

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), 6185

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), 393402.

Boundedness for surfaces in weighted projective 4spaces [ps] [pdf]
L.V. Rammea and G.K. Sankaran.
Proc. Amer. Math. Soc. 139 (2011), 33933403.

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), 463478.

Moduli spaces of irreducible symplectic manifolds [ps] [pdf]
V. Gritsenko, K. Hulek and G.K. Sankaran.
Compositio Math. 146 (2010) 404434.

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), 3952.

Numerical obstructions to abelian surfaces in toric Fano 4folds [ps] [pdf]
G.K. Sankaran.
Kodai Math. J. 31 (2008), 120.
(This, among other things, corrects the error in Abelian surfaces
in toric 4folds, below.)

HirzebruchMumford proportionality and locally symmetric varieties
of orthogonal type [ps] [pdf]
V. Gritsenko, K. Hulek and G.K. Sankaran.
Documenta Math. 13 (2008), 119.

Cusp forms: a clarification [ps] [pdf]
G.K. Sankaran.
Unpublished note, 2008. This fills a small gap, pointed out by
R. Salvati Manni, in The Kodaira dimension of the moduli of K3
surfaces below, and is put here for reference. The matter is
more fully addressed in later papers.

The Kodaira dimension of the moduli of K3 surfaces [ps] [pdf]
V. Gritsenko, K. Hulek and G.K. Sankaran.
Invent. Math. 167 (2007), 519567.
The
original publication is available at
www.springerlink.com.

The HirzebruchMumford volume for the orthogonal group and
applications [ps] [pdf]
V. Gritsenko, K. Hulek and G.K. Sankaran.
Documenta Math. 12 (2007), 215241.

The nef cone of toroidal compactifications of
A_{4} [ps] [pdf]
K. Hulek and G.K. Sankaran.
Proc. London Math. Soc. 88 (2004), 659704.

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), 279300.

The moduli space of bilevel6 abelian surfaces [ps] [pdf]
G.K. Sankaran and J. Spandaw.
Nagoya Math. J. 168 (2002), 113125.

Das Titsgebäude von Siegelschen Modulgruppen vom Geschlecht
2 [ps] [pdf]
M. Friedland and G.K. Sankaran.
Abh. Math. Sem. Univ. Hamburg 71 (2001), 4968.
(In German; but there is a supplement with an
English summary [ps]
[pdf]
and some pictures)

Algebraic construction of normalized coprime factors for delay
systems [ps] [pdf]
J.R. Partington and G.K. Sankaran.
Math. Control Signals Systems 15 (2002), 112.
(I know nothing about this subject)

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), 89156.
(A survey article)

Abelian surfaces in toric 4folds [ps] [pdf]
G.K. Sankaran.
Math. Ann. 313 (1999), 409427.
Warning: this paper contains a significant error. Here
is a correction. [ps] [pdf]

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), 177192.

Heisenberginvariant Kummer surfaces [ps] [pdf]
K. Hulek, I. Nieto and G.K. Sankaran.
Proc. Edin. Math. Soc. 43 (2000), 425439.
Other pages of mine:
Last modified 26th April, 2016.
Maintained by:
G.K.Sankaran@bath.ac.uk