Related papers: The singularities of $A_g^P$

The present work deals with the canonical map of smooth, compact complex surfaces of general type in a polarization of type $(1,2,2)$ on an abelian threefold. A natural and classical question is whether the canonical system of such surfaces…

We shall consider minimal analytic compactifications of the affine plane with singularities. In previous work, Kojima and Takahashi proved that any minimal analytic compactification of the affine plane, which has at worse log canonical…

I prove the existence, and describe the structure, of moduli space of pairs $(p,\Theta)$ consisting of a projective variety $P$ with semiabelian group action and an ample Cartier divisor on it satisfying a few simple conditions. Every…

In this paper, we discuss a generalization of log canonical singularities in the non-$\mathbb{Q}$-Gorenstein setting. We prove that if a normal complex projective variety has a non-invertible polarized endomorphism, then it has log…

We prove the following: (1) if $X$ is ordinary, the Fulton-MacPherson configuration space $X[n]$ is ordinary for all $n$; (2) the moduli of stable $n$-pointed curves of genus zero is ordinary. (3) More generally we show that a wonderful…

In this paper we compute the cohomology groups of the second Voronoi compactification of the moduli space of abelian fourfolds in all degrees with the exception of the middle degree 10. We also compute the cohomology groups of the perfect…

We study the GIT compactification $\mathbb{P}(\mathrm{Sym}^3\mathbb{C}^7)//\mathrm{SL}(7)$ of the moduli space of cubic fivefolds $X\subset\mathbb{P}^6$ and give an explicit description of its strictly semistable boundary. We construct…

We prove that the moduli space ${\mathcal A}_{g,\Gamma_0(p)}\otimes \bar {\mathbb F}_p$ of principally polarized abelian varieties of dimension $g$ with a $\Gamma_0(p)$-level structure in characteristic $p$ has $2^g$ irreducible…

Consider the moduli space $\mathcal{M}_{g}$ of Riemann surfaces of genus $g\geq 2$ and its Deligne-Munford compactification $\bar{\mathcal{M}_{g}}$. We are interested in the branch locus ${\mathcal{B}_{g}}$ for $g>2$, i.e., the subset of…

We prove that the ring of Siegel modular forms of weight divisible by g+n+1 is isomorphic to the ring of (log) pluricanonical forms on the n-fold Kuga family of abelian varieties and its certain compactifications, for every arithmetic group…

Let Z be an algebraic homogeneous space Z=G/H attached to real reductive Lie group G. We assume that Z is real spherical, i.e., minimal parabolic subgroups have open orbits on Z. For such spaces we investigate their large scale geometry and…

In this note, we aim to prove the finite semi-algebraic chamber decomposition theorem for K-semi(poly)stability under the assumption of the log boundedness of K-semistable degenerations. This boundedness assumption is naturally arising from…

We locate the complexity of the set of closed sets of uniqueness U(G), for G locally compact Lie group and of the set of closed sets of extended uniqueness U_0(G), for G connected abelian Lie group. More concretely, we prove that with…

We associate to each stable Higgs pair $(A_0,\Phi_0)$ on a compact Riemann surface $X$ a singular limiting configuration $(A_\infty,\Phi_\infty)$, assuming that $\det \Phi$ has only simple zeroes. We then prove a desingularization theorem…

We prove compactification theorems for some complete K\"ahler manifolds with nonnegative Ricci curvature. Among other things, we prove that a complete noncompact K\"ahler Ricci flat manifold with maximal volume growth and quadratic…

We construct a compactification of the universal moduli space of semistable principal $G$-bundles over $\overline{\textrm{M}}_{g}$, the fibers of which over singular curves are the moduli spaces of $\delta$-semistable singular principal…

We prove the Cone Theorem for algebraically integrable foliations. As a consequence, we show that termination of flips implies the b-nefness of the moduli part of a log canonical pair with respect to a contraction, generalising the case of…

There is a canonical isomorphism between the coarse moduli spaces of somooth hyperelliptic curves of genus g and binary forms of degree 2g+2 with nonzero discriminant. In this paper, we study the extension of this isomorphism to the…

$G_2$-monopoles are solutions to gauge theoretical equations on $G_2$-manifolds. If the $G_2$-manifolds under consideration are compact, then any irreducible $G_2$-monopole must have singularities. It is then important to understand which…

We compute the low degree $\ell$-adic intersection cohomology of symplectic local systems on the Satake compactification of the moduli space $A_g$ of principally polarized abelian varieties. We prove that only a small finite list of…