Boundedness for surfaces in weighted P^4 (2009)
Rammea, L. V., Sankaran, G. K.
Ellingsrud and Peskine (1989) proved that there exists a bound on the degree of smooth non general type surfaces in P^4. The latest proven bound is 52 by Decker and Schreyer in 2000. In this paper we...
Abelianisation of orthogonal groups and the fundamental group of modular varieties (2008)
Gritsenko, V., Hulek, K., Sankaran, G. K.
We study the commutator subgroup of integral orthogonal groups belonging to indefinite quadratic forms. We show that the index of this commutator is 2 for many groups that occur in the construction...
Moduli spaces of irreducible symplectic manifolds (2008)
Gritsenko, V., Hulek, K., Sankaran, G. K.
We study the moduli spaces of polarised irreducible symplectic manifolds. By a comparison with locally symmetric varieties of orthogonal type of dimension 20, we show that the moduli space of 2d...
The moduli space of \'etale double covers of genus 5 curves is unirational (2008)
Izadi, E., Giudice, M. Lo, Sankaran, G. K.
We show that the coarse moduli space $\cR_5$ of \'etale double covers of curves of genus~5 over the complex numbers is unirational. We give two slightly different arguments, one purely geometric and...
The Kodaira dimension of the moduli of K3 surfaces (2008)
V. Gritsenko, K. Hulek, G. K. Sankaran
The global Torelli theorem for projective K3 surfaces was first proved by Piatetskii-Shapiro and Shafarevich 35 years ago, opening the way to treating moduli problems for K3 surfaces. The moduli...
Heisenberg-invariant Kummer surfaces (2008)
K. Hulek, I. Nieto, G. K. Sankaran
We study, from the point of view of abelian and Kummer surfaces and their moduli, the special quintic threefold known as Nieto's quintic. It is in some ways analogous to the Segre cubic and the...
genus five curves MAT/03 (2008)
Facoltà Di, Scienze Matematiche, Fisiche E Naturali, Corso Di, Dottorato Di, Ricerca In Matematica, ...
The unirationality of the moduli
There are embeddings of complex abelian surfaces in P 4 (2007)
but it was shown by Van de Ven in [17] that no abelian d-fold can be embedded in P
Degenerations of (1,3) abelian surfaces and Kummer surfaces (2007)
K. Hulek, I. Nieto, G.K. Sankaran
. We study degenerations of Kummer surfaces associated to certain divisors in Nieto's quintic threefold and show how they arise from boundary components of a suitable toroidal compactication of...
Algebraic Construction of Normalized Coprime Factors for Delay Systems (2007)
J. R. Partington, G.K. Sankaran, Claverton Down, Bath Ba Ay
We introduce an algebraic approach to the problem of constructing explicit normalized coprime factorizations for retarded delay systems. A parametrization is given of all the possible factorizations...
K. Hulek, I. Nieto, G. K. Sankaran
We study degenerations of Kummer surfaces associated to certain divisors in Nieto's quintic threefold and show how they arise from boundary components of a suitable toroidal compacti cation of...
Numerical obstructions to abelian surfaces in toric Fano 4-folds (2007)
Some of the 124 toric Fano 4-folds contain abelian surfaces but most do not: in a few cases it is not known whether they do or not. By elementary methods, with a little computer help, we exclude some...
Any smooth toric threefold contains all curves (2007)
We show that If X is a smooth projective toric threefold and Y is a smooth projective curve then Y can be embedded in X. This partially answers a question raised by Eisenbud and Harris.
Numerical obstructions to abelian surfaces in toric Fano 4-fold (2007)
This paper is withdrawn because it is superseded by arXiv:0710.4284
Numerical obstructions to abelian surfaces in toric (2007)
On the list of smooth toric Fano 4-folds ([1, 12]), of which there are 124, there remain 19 for which it is not known whether there are embedded abelian surfaces. In order to avoid trivialities, we...
Hirzebruch-Mumford proportionality and locally symmetric varieties of orthogonal type (2006)
Gritsenko, V., Hulek, K., Sankaran, G. K.
For many classical moduli spaces of orthogonal type there are results about the Kodaira dimension. But nothing is known in the case of dimension greater than 19. In this paper we obtain the first...
The Kodaira dimension of the moduli of K3 surfaces (2006)
Gritsenko, V., Hulek, K., Sankaran, G. K.
The moduli space of polarised K3 surfaces of degree 2d is a quasi-projective variety of dimension 19. For general d very little has been known about the Kodaira dimension of these varieties. In this...
The Hirzebruch-Mumford volume for the orthogonal group and applications (2005)
Gritsenko, Valery, Hulek, Klaus, Sankaran, G. K.
In this paper we derive an explicit formula for the Hirzebruch-Mumford volume of an indefinite lattice L of rank at least 3. If \Gamma is an arithmetic subgroup of the group O(L) of isometries of L...
Abelian Surfaces With Odd Bilevel Structure (2003)
G.K. Sankaran, Kodaira Dimension (a, Theorem A
this paper we examine the Kodaira dimension (A t ) for larger t. Our main result is the following (Theorem VIII.1)
In lieu of birthday greetings (2003)
Birch, B. J., Colliot-Thlne, Jean-Louis, Sankaran, G. K., Reid, Miles, Skorobogatov, Alexei
Abelian surfaces with odd bilevel structure (2002)
The moduli space of abelian surfaces with polarisation of type (1,t) and a bilevel structure is of general type if t is odd and at least 17.
The nef cone of toroidal compactifications of ${\cal A}_4$ (2002)
We determine the cone of nef divisors on the Igusa and Voronoi compactifications of the moduli space of principally polarised abelian 4-folds. We also show that the canonical bundle on the Igusa...
The moduli space of bilevel-6 abelian surfaces (2002)
Sankaran, G. K., Spandaw, J. G.
We show that the moduli space of abelian surfaces with polarisation of type $(1, 6)$ and a bilevel structure has positive Kodaira dimension and indeed $p_{g} \geq 3$. To do this we show that three of...
The Moduli Space of Bilevel-6 Abelian Surfaces (2002)
Sankaran Spandaw The, G. K. Sankaran, J. G Sp
ieto threefold is Calabi-Yau. We also derive some information about divisors in X 6 and linear relations among them. Acknowledgement: We are grateful to the DAAD and the British Council for nancial...
The Nef Cone of Toroidal Compactifications of A4 (2002)
The moduli space... In this paper, we shall be mainly interested in the Voronoi compactification A4^Vor of A4 . This is a natural choice from the point of view of moduli in view of the results of...
Algebraic Construction of Normalized Coprime Factors for Delay Systems (2001)
J. R. Partington, G. K. Sankaran, Claverton Down, Bath Ba Ay
We introduce an algebraic approach to the problem of constructing explicit normalized coprime factorizations for retarded delay systems.
The moduli space of bilevel-6 abelian surfaces (2000)
Sankaran, G. K., Spandaw, J. G.
The moduli space of abelian surfaces with polarisation of type (1,6) and a bilevel structure has positive Kodaira dimension. By contrast, Mukai has shown that the moduli space of bilevel-t abelian...
Das Titsgebaeude von Siegelschen Modulgruppen vom Geschlecht 2 (2000)
Friedland, M., Sankaran, G. K.
We calculate Tits buildings for certain arithmetic subgroups of Sp(4). These give information about the boundary of the corresponding moduli spaces of abelian surfaces. More pictures (in colour) and...
The geometry of Siegel modular varieties (1998)
This is a survey article about Siegel modular varieties over the complex numbers. It is written mostly from the point of view of moduli of abelian varieties, especially surfaces. We cover...
Abelian surfaces in toric 4-folds (1998)
We investigate the possibility of embedding minimal abelian surfaces in smooth toric 4-folds with Picard number 2. The existence of such an embedding imposes conditions on the 4-fold, which we partly...
The Geometry of Siegel Modular Varieties (1998)
this article and would have led us beyond the areas where we can pretend to competence.
Heisenberg-invariant Kummer surfaces (1997)
Hulek, K., Nieto, I., Sankaran, G. K.
We study the geometry of Nieto's quintic threefold (Barth & Nieto, J. Alg. Geom. 3, 1994) and the Kummer and abelian surfaces that correspond to special loci.
Degenerations of (1,3) abelian surfaces and Kummer surfaces (1997)
Hulek, K., Nieto, I., Sankaran, G. K.
We continue our study of the geometry of Nieto's quintic threefold, looking at degenerate surfaces that correspond to certain loci and showing how they arise from a toroidal compactification of a...
Fundamental group of locally symmetric varieties (1995)
Take a bounded symmetric domain $D$ and an arithmetic subgroup $\Gamma$ of ${\rm Aut}(D)$. Take the quotient $D/\Gamma$, compactify and resolve the singularities. We study the fundamental group of...
Moduli of Polarised Abelian Surfaces (1994)
The toroidal compactification of the moduli space of complex abelian surfaces with a polarisation of type (1,p), p a prime, is of general type if p is at least 173. Happy Christmas.
Moduli of abelian surfaces with a $(1,p^2)$ polarisation (1994)
Gritsenko, V. A., Sankaran, G. K.
We show that the (compactified) moduli space of abelian surfaces with a polarisation of type $(1,p^2)$ is of general type for $p \ge 11$, improving a result of O'Grady.
The Fundamental Group of Some Siegel Modular Threefolds (1994)
Let A be the moduli space of (1,p)-polarised abelian surfaces with a level structure, for p an odd prime. Let X be a desingularisation of any algebraic compactification of A. Then X is...
Heisenberg-invariant Kummer surfaces
K. Hulek, I. Nieto, G.K. Sankaran
this paper we study, from the point of view of abelian surfaces and their moduli, the special quintic threefold N rst described in [Ni1] and [BN], known as Nieto's quintic
Heisenberg-invariant Kummer surfaces
Hulek Nieto Sankaran, K. Hulek, I. Nieto, G. K. Sankaran
this paper we study, from the point of view of abelian surfaces and their moduli, the special quintic threefold N first described in [Ni1] and [BN], known as Nieto's quintic . Nieto's...
The Geometry of Siegel Modular Varieties
this article and would have led us beyond the areas where we can pretend to competence