Related papers: Projective spaces in Fermat varieties
We study birational maps among 1) the moduli space of semistable torsion sheaves of Hilbert polynomial $4m+2$ on a smooth quadric surface, 2) the moduli space of semistable torsion sheaves of Hilbert polynomial $m^{2}+3m+2$ on…
Some sharp inequalities of Gruss type for sequences of vectors in real or complex normed linear spaces are obtained. Applications for the discrete Fourier and Mellin transform are given. Estimates for polynomials with coefficients in normed…
We survey some aspects of stability conditions both in general and on the derived category of coherent sheaves on a surface, with applications to the birational geometry of certain holomorphic symplectic varieties.
We shall study moduli spaces of stable 1-dimensional sheaves on an elliptic ruled surface.
We prove an unobstructedness result for deformations of subvarieties constrained by intersections with another, fixed subvariety. We deduce smoothness and expected-dimension results for multiple-point loci of generic projections, mainly…
In this note, we make a step towards the classification of toric surfaces admitting reducible Severi varieties. We generalize the results of [Lan19, Tyo13, Tyo14], and provide two families of toric surfaces admitting reducible Severi…
We determine set theoretic defining equations for the third secant variety of the Segre product of $n$ projective spaces, and from the proof of the main statement we derive an upper bound for the degrees of these equations.
Each of the four critical Severi varieties arises from a minimal holomorphic nilpotent orbit in a simple regular rank 3 hermitian Lie algebra and each such variety lies as singular locus in a cubic--the chordal variety--in the corresponding…
We provide a classification of complex projective surfaces with a holomorphic foliation whose group of birational symetries is infinite.
A symplectic structure on the space of nondegenerate and nonparametrized curves in a locally affine manifold is defined. We also consider several interesting spaces of nondegenerate projective curves endowed with Poisson structures. This…
We express nested Hilbert schemes of points and curves on a smooth projective surface as "virtual resolutions" of degeneracy loci of maps of vector bundles on smooth ambient spaces. We show how to modify the resulting obstruction theories…
We calculate a projective space of essential measured laminations in a surface pair, which will be used in another paper to help describe spaces of "finite height laminations."
We show that certain semistable sheaves on the projective plane with linear Hilbert polynomial are cokernels of semistable morphisms of decomposable sheaves.We exhibit certain locally closed subvarieties of moduli spaces of semistable…
The purpose of this paper is to use conservative descent to study semi-orthogonal decompositions for some homogeneous varieties over general bases. We produce a semi-orthogonal decomposition for the bounded derived category of coherent…
In this short note we prove a sector counting lemma for a class of Fermi surface on the plane which are $C^2$-differentiable and strictly convex. This result generalizes the one proved in \cite{FKT} for the class of…
For a hypersurface in a projective space, we consider the set of pairs of a point and a line in the projective space such that the line intersects the hypersurface at the point with a fixed multiplicity. We prove that this set of pairs…
In this paper we extend the well known theorem of Angelo Lopez concerning the Picard group of the general space projective surface containing a given smooth projective curve, to the intermediate N\'eron-Severi group of a general…
We study the space of rational curves on del Pezzo surfaces in positive characteristic. For most primes p we prove the irreducibility of the moduli space of rational curves of a given nef class, extending results of Testa in characteristic…
We study the problem of characterizing linear preserver subgroups of algebraic varieties, with a particular emphasis on secant varieties and other varieties of tensors. We introduce a number of techniques built on different geometric…
We study the restricted families of projections in vector spaces over finite fields. We show that there are families of random subspaces which admit a Marstrand-Mattila type projection theorem.