Related papers: On the log minimal model program for irreducible s…

In this paper, we prove a minimal modularity lifting theorem for Galois representations (conjecturally) associated to Siegel modular forms of genus two which are holomorphic limits of discrete series at infinity.

We show the validity of two special cases of the four-dimensional Minimal Model Program in characteristic $p>5$: for contractions to $\mathbb{Q}$-factorial fourfolds and in families over curves ("semi-stable mmp"). We also provide their…

Exploiting recent results on the ample cone of irreducible symplectic manifolds, we provide a different point of view for the computation of their monodromy groups. In particular, we give the final step in the computation of the monodromy…

We show that minimal models of $\mathbb{Q}$-factorial NQC log canonical generalised pairs exist, assuming the existence of minimal models of smooth varieties. More generally, we prove that on a $\mathbb{Q}$-factorial NQC log canonical…

We study a linear elliptic differential operator of the form $\mathcal{P}=\Delta + V - \lambda$ on a quasi-asymptotically conical manifold $(M, g)$, where $g$ is a polyhomogeneous metric and $V$ is a $b$-vector field that is unbounded with…

We construct a moduli space of stable projective pairs with a nontrivial action of a connected reductive group. These stable reductive pairs are higher-dimensional analogs of stable n-pointed curves and generalize to the non-commutative…

In this paper we study complex symplectic manifolds, i.e., compact complex manifolds $X$ which admit a holomorphic $(2, 0)$-form $\sigma$ which is $d$-closed and non-degenerate, and in particular the Beauville-Bogomolov-Fujiki quadric…

Using our previous results on the systematic construction of invariant differential operators for non-compact semisimple Lie groups we classify the special reduced multiplets and minimal representations in the case of SO(p,q).

We obtain a standard local presentation for a vector-valued multisymplectic form on a smooth manifold, generalizing the known proof for polysymplectic forms. We show that vector-valued multisymplectic forms on a finite-dimensional real…

We prove the existence of pl-flips.

Let $(X,\omega)$ be a compact symplectic manifold, $L$ be a Lagrangian submanifold and $V$ be a codimension 2 symplectic submanifold of $X$, we consider the pseudoholomorphic maps from a Riemann surface with boundary…

Let $X$ be a compact K\"ahler manifold and $D$ be a simple normal crossing divisor. If $D$ is the support of some effective $k$-ample divisor, we show $$ H^q(X,\Omega^p_X(\log D))=0,\quad \text{for}\quad p+q>n+k.$$

We shall give an example of irreducible symplectic manifolds X and Y which are not bimeromorphic, but have the same periods in the second cohomologies. More explicitly, X and Y are generalized Kummer varieties of dim 4 for a general complex…

We compute the minimal log discrepancies of determinantal varieties of square matrices, and more generally of pairs $\bigl(D^k,\sum \alpha_i D^{k_i}\bigr)$ consisting of a determinantal variety (of square matrices) and an $\mathbb R$-linear…

The semistable minimal model program is a special case of the minimal model program concerning 3-folds fibred over a curve and birational morphisms preserving this structure. We classify semistable divisorial contractions which contract the…

In this paper, we show that for any projective klt pair $(X,\Delta)$ over an algebraically closed field of characteristic \(0\) and any big $\mathbb{Q}$-Cartier $\mathbb{Q}$-divisor $L$ on $X$, the invariants $\alpha(X,\Delta,L)$ and…

We establish a local model for the moduli space of holomorphic symplectic structures with logarithmic poles, near the locus of structures whose polar divisor is normal crossings. In contrast to the case without poles, the moduli space is…

We give a topological bound on the number of minimal models of a class of three dimensional log smooth pairs of general type.

In this article we prove that if $(X,B+\beta)$ is a projective generalized klt pair such that $B+\beta$ is big, then $(X,B+\beta)$ admits a good Minimal Model or Mori fiber space. In particular, this implies Tossati's transcendental…

We prove that the non-vanishing conjecture and the log minimal model conjecture for projective log canonical pairs can be reduced to the non-vanishing conjecture for smooth projective varieties such that the boundary divisor is zero.