Search results for " sheaves"
showing 7 items of 7 documents
A closed formula for the evaluation of foams
2020
International audience; We give a purely combinatorial formula for evaluating closed, decorated foams. Our evaluation gives an integral polynomial and is directly connected to an integral, equivariant version of colored Khovanov-Rozansky link homology categorifying the sl(N) link polynomial. We also provide connections to the equivariant cohomology rings of partial flag varieties.
Logarithmic bundles of deformed Weyl arrangements of type $A_2$
2016
We consider deformations of the Weyl arrangement of type $A_2$, which include the extended Shi and Catalan arrangements. These last ones are well-known to be free. We study their sheaves of logarithmic vector fields in all other cases, and show that they are Steiner bundles. Also, we determine explicitly their unstable lines. As a corollary, some counter-examples to the shift isomorphism problem are given.
Moduli spaces of quasitrivial sheaves on the three dimensional projective space
2022
Let M(r,c_1,c_3,c_3) denote the Gieseker--Maruyama moduli space of semistable rank r sheaves on P^3 with the first, second and third Chern classes equal to c_1, c_2 and c_3, respectively. Maruyama proved that the space M(r,c_1,c_3,c_3) is a projective scheme. However, the geometry of such a scheme remains largely unknown, despite the efforts of many authors in the past four decades, and questions about connectedness, irreducibility, the number of irreducible components, and so on, remain open.When r=1 and c_1=0 (which can always be achieved after twisting by an appropriate line bundle), one gets that M(1,0,c_2,c_3) is isomorphic to the Hilbert scheme Hilb^{d,g}(P^3) of 1-dimensional schemes…
On stability of logarithmic tangent sheaves. Symmetric and generic determinants
2021
We prove stability of logarithmic tangent sheaves of singular hypersurfaces D of the projective space with constraints on the dimension and degree of the singularities of D. As main application, we prove that determinants and symmetric determinants have stable logarithmic tangent sheaves and we describe an open dense piece of the associated moduli space.
Lawvere–Tierney sheaves in Algebraic Set Theory
2009
We present a solution to the problem of defining a counterpart in Algebraic Set Theory of the construction of internal sheaves in Topos Theory. Our approach is general in that we consider sheaves as determined by Lawvere-Tierney coverages, rather than by Grothendieck coverages, and assume only a weakening of the axioms for small maps originally introduced by Joyal and Moerdijk, thus subsuming the existing topos-theoretic results.
Ulrich bundles on K3 surfaces
2019
We show that any polarized K3 surface supports special Ulrich bundles of rank 2.
The associated sheaf functor theorem in algebraic set theory
2008
We prove a version of the associated sheaf functor theorem in Algebraic Set Theory. The proof is established working within a Heyting pretopos equipped with a system of small maps satisfying the axioms originally introduced by Joyal and Moerdijk. This result improves oil the existing developments by avoiding the assumption of additional axioms for small maps and the use of collection sites.