Related papers: Contact loci in arc spaces
In this paper we develop a method for studying tight contact structures on lens spaces. We then derive uniqueness and non-existence statements for tight contact structures with certain (half) Euler classes on lens spaces. We also prove that…
Let $C$ be an irreducible algebraic curve defined over a number field and inside an algebraic torus of dimension at least 3. We partially answer a question posed by Levin on points on $C$ for which a non-trivial power lies again on $C$. Our…
The higher Nash blowup of an algebraic variety replaces singular points with limits of certain spaces carrying higher-order data associated to the variety at non-singular points. In this note we will define a higher-order Jacobian matrix…
We explore the relation between the positive dimensional irreducible components of the characteristic varieties of rank one local systems on a smooth surface and the associated (rational or irrational) pencils. Our study, which may viewed…
Rectangular designs are classified as regular, Latin regular, semiregular, Latin semiregular and singular designs. Some series of selfdual as well as alpharesolvable designs are obtained using matrix approaches which belong to the above…
The paper is devoted to the complete classification of all real Lie algebras of contact vector fields on the first jet space of one-dimensional submanifolds in the plane. This completes Sophus Lie's classification of all possible Lie…
Symplectic fillings of standard tight contact structures on lens spaces are understood and classified. The situation is different if one considers non-standard tight structures (i.e. those that are virtually overtwisted), for which a…
Here we consider a Cahn-Hilliard-Navier-Stokes system characterized by a nonlocal Cahn-Hilliard equation with a singular (e.g., logarithmic) potential. This system originates from a diffuse interface model for incompressible isothermal…
We compare two partitions of real bitangents to smooth plane quartics into sets of 4: one coming from the closures of connected components of the avoidance locus and another coming from tropical geometry. When both are defined, we use the…
The equation $x^m = 0$ defines a fat point on a line. The algebra of regular functions on the arc space of this scheme is the quotient of $k[x, x', x^{(2)}, \ldots]$ by all differential consequences of $x^m = 0$. This infinite-dimensional…
The bad locus and the rude locus of an ample and base point free linear system on a smooth complex projective variety are introduced and studied. The bad locus is defined as the set of points that force divisors through them to be…
We establish a connection between properties of partially symmetric tensors (i.e. tensors associated to linear systems of quadric hypersurfaces) and the geometry of some related loci, generalization of the Weddle loci introduced in…
The quotient of a finite-dimensional vector space by the action of a finite subgroup of automorphisms is usually a singular variety. Under appropriate assumptions, the McKay correspondence relates the geometry of nice resolutions of…
It is well known that knots are countable in ordinary knot theory. Recently, knots {\it with intersections} have raised a certain interest, and have been found to have physical applications. We point out that such knots --equivalence…
This paper studies the Cauchy problem for a helical vortex filament evolving by the 3D incompressible Navier-Stokes equations. We prove global-in-time well-posedness and smoothing of solutions with initial vorticity concentrated on a helix.…
In this paper, we study the singularities of a pair (X,Y) in arbitrary characteristic via jet schemes. For a smooth variety X in characteristic 0, Ein, Lazarsfeld and Mustata showed that there is a correspondence between irreducible closed…
We study polynomials with complex coefficients which are nondegenerate in two senses, one of Kouchnirenko and the other with respect to its Newton polyhedron, through data on contact loci and motivic nearby cycles. Introducing an explicit…
The paper investigates the locus of non-simple principally polarised abelian $g$-folds. We show that the irreducible components of this locus are $\Is^g_{D}$, defined as the locus of principally polarised $g$-folds having an abelian…
We study the loci of principally polarized abelian varieties with points of high multiplicity on the theta divisor. Using the heat equation and degeneration techniques, we relate these loci and their closures to each other, as well as to…
Let (S,H) be a polarized K3 surface, $E$ be a coherent sheaf on S and W be a linear subspace in the space of global sections H^0(S,E). If we are lucky, there is an exact sequence 0 -> W tensor O -> E -> E' -> 0, which gives a correspondence…