Macaulay's theorem and local Torelli for weighted hypersurfaces
Manin’s conjecture for a quartic del Pezzo surface with singularity
The Manin conjecture is established for a split singular del Pezzo surface of degree four, with singularity type .
Manin’s conjecture for a singular sextic del Pezzo surface
We prove Manin’s conjecture for a del Pezzo surface of degree six which has one singularity of type . Moreover, we achieve a meromorphic continuation and explicit expression of the associated height zeta function.
Manin's conjecture on a nonsingular quartic del Pezzo surface
Mapping threefolds onto three-dimensional quadrics.
Maps onto certain Fano threefolds.
Matrix factorizations and singularity categories for stacks
We study matrix factorizations of a potential W which is a section of a line bundle on an algebraic stack. We relate the corresponding derived category (the category of D-branes of type B in the Landau-Ginzburg model with potential W) with the singularity category of the zero locus of W generalizing a theorem of Orlov. We use this result to construct push-forward functors for matrix factorizations with relatively proper support.
Matrix factorizations for domestic triangle singularities
Working over an algebraically closed field k of any characteristic, we determine the matrix factorizations for the-suitably graded-triangle singularities of domestic type, that is, we assume that (a,b,c) are integers at least two satisfying 1/a + 1/b + 1/c > 1. Using work by Kussin-Lenzing-Meltzer, this is achieved by determining projective covers in the Frobenius category of vector bundles on the weighted projective line of weight type (a,b,c). Equivalently, in a representation-theoretic context,...
Maximal Cohen--Macaulay modules over hypersurface rings.
Maximal Mordell-Weil lattices of fibred surfaces with
Maximal Orders of global dimension and Krull dimension two.
Maximal rationally connected fibrations and movable curves
A well known result of Miyaoka asserts that a complex projective manifold is uniruled if its cotangent bundle restricted to a general complete intersection curve is not nef. Using the Harder-Narasimhan filtration of the tangent bundle, it can moreover be shown that the choice of such a curve gives rise to a rationally connected foliation of the manifold. In this note we show that, conversely, a movable curve can be found so that the maximal rationally connected fibration of the manifold may be recovered...
Mémoire sur une transformation géométrique et sur la surface des ondes.
Méthodes et résultats effectifs en géométrie algébrique
Métriques d'Einstein-Kähler sur les variétés de Fano : obstructions et existence
Minimal models and the Kodaira dimension of algebraic fiber spaces.
Minimal models of algebraic threefolds : Mori's program
Minimal models of foliated algebraic surfaces
Minimal resolution of general stable rank-2 vector bundles on
We study general elements of moduli spaces of rank-2 stable holomorphic vector bundles on and their minimal free resolutions. Incidentally, a quite easy proof of the irreducibility of is shown.
Minimal sections of conic bundles
Sia un fibrato in coniche standard con curva discriminante di grado . La varietà delle sezioni minime delle superfici , dove è una curva di grado , si spezza in due componenti e . Si prova che, mediante la mappa di Abel-Jacobi , una di queste componenti domina la Jacobiana intermedia , mentre l'altra domina il divisore theta . Questi risultati vengono applicati ad alcuni threefold di Fano birazionalmente equivalenti a un fibrato in coniche. In particolare si prova che il generico...