Let M be a Kobayashi-hyperbolic 2-dimensional complex manifold and Aut(M) the group of holomorphic automorphisms of M . We showed earlier that if dimAut(M) = 3, then Aut(M)-orbits are closed submanifolds in M of (real) codimension 1 or 2. In a preceding article we classified all such manifolds in the case when every orbit has codimension 1. In the present paper we complete the classification by...

We develop the foundation of the complex symplectic geometry of Lagrangian subvarieties in a hyperkähler manifold. We establish a characterization, a Chern number inequality, topological and geometrical properties of Lagrangian submanifolds. We discuss a category of Lagrangian subvarieties and its relationship with the theory of Lagrangian intersection. We also introduce and study extensively a...

In [4, Definition 8.1], some important subvarieties of the variety SH of semi-Heyting algebras are defined. The purpose of this paper is to introduce and investigate the subvariety ISSH of SH, characterized by the identity (0  1)  (0  1)  1. We prove that ISSH contains all the subvarieties introduced by Sankappanavar and it is in fact the least subvariety of SH with this property. We als...

Let [ ] denote a linear code over with length , codimension , and covering radius . We use a modification of constructions of [2 +1 2 3] 2 and [3 +1 3 5] 3 codes ( 5) to produce infinite families of good codes with covering radius 2 and 3 and codimension .

Let $\Gamma \subset \mathrm{PU}(1,n)$ be a lattice and $S_\Gamma$ the associated ball quotient. We prove that, if contains infinitely many maximal complex totally geodesic subvarieties, then $\Gamma$ is arithmetic. also an Ax--Schanuel Conjecture for $S_\Gamma$, similar to one recently proven by Mok, Pila Tsimerman. One of main ingredients in proofs realise inside period domain polarised integr...

We show that certain geometrically defined higher codimension cycles are extremal in the effective cone of the moduli spaceMg,n of stable genus g curves with n ordered marked points. In particular, we prove that codimension two boundary strata are extremal and exhibit extremal boundary strata of higher codimension. We also show that the locus of hyperelliptic curves with a marked Weierstrass po...

The study of semigroup algebras has a long tradition in commutative algebra. Presentation ideals of semigroup algebras are called toric ideals, in reference to their prominent role in geometry. In this paper we consider the more general class of lattice ideals. Fix a polynomial ring S = k[x1, . . . , xn] over a field k and identify monomials x in S with vectors a ∈ N. Let L be any sublattice of...

Torelli space Tg (g ≥ 2) is the quotient of Teichmüller space by the Torelli group Tg. It is the moduli space of compact, smooth genus g curves C together with a symplectic basis of H1(C;Z) and is a model of the classifying space of Tg. Mess, in his thesis [12], proved that T2 has the homotopy type of a bouquet of a countable number of circles. Johnson and Millson (cf. [12]) pointed out that a ...