The moduli space of special lagrangian submanifolds
The moduli space of totally marked degree two rational maps
A rational map ϕ: ℙ¹ → ℙ¹ along with an ordered list of fixed and critical points is called a totally marked rational map. The space of totally marked degree two rational maps can be parametrized by an affine open subset of (ℙ¹)⁵. We consider the natural action of SL₂ on induced from the action of SL₂ on (ℙ¹)⁵ and prove that the quotient space exists as a scheme. The quotient is isomorphic to a Del Pezzo surface with the isomorphism being defined over ℤ[1/2].
The moduli spaces of polarized abelian varieties.
The Moduli spaces of Rank 2 Stable Vector Bundles over Veronesean surfaces.
The Moduli Spaces of Vector Bundles over an Algebraic Curve.
The moment problem for non-compact semialgebraic sets.
The monodromy conjecture for zeta functions associated to ideals in dimension two
The monodromy conjecture states that every pole of the topological (or related) zeta function induces an eigenvalue of monodromy. This conjecture has already been studied a lot. However in full generality it is proven only for zeta functions associated to polynomials in two variables.In this article we work with zeta functions associated to an ideal. First we work in arbitrary dimension and obtain a formula (like the one of A’Campo) to compute the “Verdier monodromy” eigenvalues associated to an...
The Monodromy of a Curve with Ordinary Double Points.
The Monodromy of a Degenerating Family of Curves.
The monodromy of a series of hypersurface singularities.
The Monodromy of Reducible Plane Curves.
The monodromy of Weierstrass points.
The Monodromy of Weighted Homogeneous Singularities
The Monodromy Weight Filtration for a Several Variables Degeneration of Hodge Structures of Weight Two.
The Mordell conjecture revisited
The Mordell–Lang question for endomorphisms of semiabelian varieties
The Mordell–Lang conjecture describes the intersection of a finitely generated subgroup with a closed subvariety of a semiabelian variety. Equivalently, this conjecture describes the intersection of closed subvarieties with the set of images of the origin under a finitely generated semigroup of translations. We study the analogous question in which the translations are replaced by algebraic group endomorphisms (and the origin is replaced by another point). We show that the conclusion of the Mordell–Lang...
The Mukai conjecture for log Fano manifolds
For a log Fano manifold (X,D) with D ≠ 0 and of the log Fano pseudoindex ≥2, we prove that the restriction homomorphism Pic(X) → Pic(D 1) of Picard groups is injective for any irreducible component D 1 ⊂ D. The strategy of our proof is to run a certain minimal model program and is similar to Casagrande’s argument. As a corollary, we prove that the Mukai conjecture (resp. the generalized Mukai conjecture) implies the log Mukai conjecture (resp. the log generalized Mukai conjecture).
The Mukai pairing. I: A categorical approach.
The multiple conical surfaces.
The multipliers of similitudes and the Brauer group of homogeneous varieties.