Related papers: Cusps of Picard modular surfaces

Irregular cusp of an orthogonal modular variety is a cusp where the lattice for Fourier expansion is strictly smaller than the lattice of translation. Presence of such a cusp affects the study of pluricanonical forms on the modular variety…

We consider minimal compact complex surfaces S with Betti numbers b_1=1 and n=b_2>0. A theorem of Donaldson gives n exceptional line bundles. We prove that if in a deformation, these line bundles have sections, S is a degeneration of…

We construct new examples of immersed minimal surfaces with catenoid ends and finite total curvature, of both genus zero and higher genus. In the genus zero case, we classify all such surfaces with at most $2n+1$ ends, and with symmetry…

We classify minimal surfaces $S$ of general type with $p_g=q=2$ and $K_S^2=6$ whose Albanese map is a generically finite double cover. We show that the corresponding moduli space is the disjoint union of three generically smooth,…

We study the collection of points on the modular surface obtained from the logarithm embeddings of the groups of units in totally real cubic number fields. We conjecture that this set is dense and show that its closure contains countably…

Let $\pi:Z\rightarrow\mathbb{P}^{n-1}$ be a general minimal $n$-fold conic bundle with a hypersurface $B_Z\subset\mathbb{P}^{n-1}$ of degree $d$ as discriminant. We prove that if $d\geq 4n+1$ then $-K_Z$ is not pseudo-effective, and that if…

We study log canonical models of foliated surfaces of general type. In particular, we show that log canonical models of general type and their minimal partial du Val resolutions are bounded. Moreover, we show the valuative criteria of…

In this article we verify an orbifold version of a conjecture of Nimershiem from 1998. Namely, for every flat $n$-manifold $M$, we show that the set of similarity classes of flat metrics on $M$ which occur as a cusp cross-section of a…

We show that if a compact complex surface admits a locally conformally flat metric, then it cannot contain a smooth rational curve of odd self-intersection. In particular, the surface has to be minimal. Then we give a list of possibilities…

We study the moduli space of smooth complete intersections of two quadrics in $\mathbb{P}^n$ by relating it to the geometry of the singular members of the corresponding pencils. Giving an alternative presentation for the moduli space of…

We determine the excluded minors characterising the class of countable graphs that embed into some compact surface.

We construct the moduli space of cubic surfaces which do not admit a Sylvester form as an arithmetic quotient, and determine the graded ring of modular forms of even weights.

Gives the most precise available description of the p-Frattini module for any p-perfect finite group G=G_0 (Thm. 2.8), and therefore of the groups G_{k,ab}, k \ge 0, from which we form the abelianized M(odular) T(ower). \S 4 includes a…

We study divisors on moduli spaces of cubic fourfolds with simple singularities and of quasi-polarized K3 surfaces of degree $2d$. For the moduli space of cubic fourfolds, we introduce a slope quantity to characterize the effective cone and…

Given a closed Riemannian manifold $(N^{n+1},g)$, $n+1 \geq 3$ we prove the compactness of the space of singular, minimal hypersurfaces in $N$ whose volumes are uniformly bounded from above and the $p$-th Jacobi eigenvalue $\lambda_p$'s are…

If $D$ is the definite quaternion algebra over $\qu$ of discriminant $p$, we compute, for any prime $p>3$, the number of infinite dimensional cusp forms on $D^*$ which are trivial at infinity, tamely ramified at $p$, and have given…

Weierstrass representation is a classical parameterization of minimal surfaces. However, two functions should be specified to construct the parametric form in Weierestrass representation. In this paper, we propose an explicit parametric…

Let $S$ be a minimal surface of general type with irregularity $q(S) = 1$. Well-known inequalities between characteristic numbers imply that $3 p_g(S) \le c_2(S) \le 10 p_g(S)$, where $p_g(S)$ is the geometric genus and $c_2(S)$ the…

Given an oriented surface of positive genus with finitely many punctures, we classify the finite orbits of the mapping class group action on the moduli space of semisimple complex special linear two dimensional representations of the…

In this note, we prove the existence of one particular class of starshaped compact hypersurfaces, by deriving global curvature estimates for such hypersurfaces; this generalizes the main result in [Hypersurfaces of prescribed mixed…