Pełnotekstowe zasoby PLDML oraz innych baz dziedzinowych są już dostępne w nowej Bibliotece Nauki.
Zapraszamy na https://bibliotekanauki.pl
Preferencje help
Widoczny [Schowaj] Abstrakt
Liczba wyników

Znaleziono wyników: 11

Liczba wyników na stronie
first rewind previous Strona / 1 next fast forward last

Wyniki wyszukiwania

help Sortuj według:

help Ogranicz wyniki do:
first rewind previous Strona / 1 next fast forward last
1
Content available remote

A note on a Brill-Noether locus over a non-hyperelliptic curve of genus 4

100%
Open Mathematics
|
2009
|
tom 7
|
nr 4
617-622
EN
We prove that a certain Brill-Noether locus over a non-hyperelliptic curve C of genus 4, is isomorphic to the Donagi-Izadi cubic threefold in the case when the pencils of the two trigonal line bundles of C coincide.
2
Content available remote

SUX(r, L) is separably unirational

100%
Open Mathematics
|
2009
|
tom 7
|
nr 1
59-60
EN
We show that the moduli space of SUX (r, L) of rank r bundles of fixed determinant L on a smooth projective curve X is separably unirational.
3
Content available remote

Λ-modules and holomorphic Lie algebroid connections

100%
Open Mathematics
|
2012
|
tom 10
|
nr 4
1422-1441
EN
Let X be a complex smooth projective variety, and G a locally free sheaf on X. We show that there is a one-to-one correspondence between pairs (Λ, Ξ), where Λ is a sheaf of almost polynomial filtered algebras over X satisfying Simpson’s axioms and $ \equiv :Gr\Lambda \to Sym \bullet _{\mathcal{O}_X } \mathcal{G}$ is an isomorphism, and pairs (L, Σ), where L is a holomorphic Lie algebroid structure on $\mathcal{G}$ and Σ is a class in F 1 H 2(L, ℂ), the first Hodge filtration piece of the second cohomology of L. As an application, we construct moduli spaces of semistable flat L-connections for any holomorphic Lie algebroid L. Particular examples of these are given by generalized holomorphic bundles for any generalized complex structure associated to a holomorphic Poisson manifold.
4
100%
Open Mathematics
|
2012
|
tom 10
|
nr 4
1306-1313
EN
Let C be a smooth projective curve over an algebraically closed field of arbitrary characteristic. Let M r,Lss denote the projective coarse moduli scheme of semistable rank r vector bundles over C with fixed determinant L. We prove Pic(M r,Lss) = ℤ, identify the ample generator, and deduce that M r,Lss is locally factorial. In characteristic zero, this has already been proved by Drézet and Narasimhan. The main point of the present note is to circumvent the usual problems with Geometric Invariant Theory in positive characteristic.
5
100%
EN
Symplectic instanton vector bundles on the projective space ℙ3 constitute a natural generalization of mathematical instantons of rank-2. We study the moduli space I n;r of rank-2r symplectic instanton vector bundles on ℙ3 with r ≥ 2 and second Chern class n ≥ r, n ≡ r (mod 2). We introduce the notion of tame symplectic instantons by excluding a kind of pathological monads and show that the locus I n;r* of tame symplectic instantons is irreducible and has the expected dimension, equal to 4n(r + 1) −r(2r + 1).
6
100%
Open Mathematics
|
2012
|
tom 10
|
nr 4
1188-1197
EN
We review a construction of Ellingsrud-Strømme relating instantons of charge n on the ordinary projective space and theta-characteristics on a plane curve of degree n with some extra-structure.
7
Content available remote

Elliptic curves on spinor varieties

76%
Open Mathematics
|
2012
|
tom 10
|
nr 4
1393-1406
EN
We prove irreducibility of the scheme of morphisms, of degree large enough, from a smooth elliptic curve to spinor varieties. We give an explicit bound on the degree.
8
Content available remote

Bubble tree compactification of moduli spaces of vector bundles on surfaces

76%
EN
We announce some results on compactifying moduli spaces of rank 2 vector bundles on surfaces by spaces of vector bundles on trees of surfaces. This is thought as an algebraic counterpart of the so-called bubbling of vector bundles and connections in differential geometry. The new moduli spaces are algebraic spaces arising as quotients by group actions according to a result of Kollár. As an example, the compactification of the space of stable rank 2 vector bundles with Chern classes c 1 = 0, c 1 = 2 on the projective plane is studied in more detail. Proofs are only indicated and will appear in separate papers.
9
Content available remote

Symplectic structures on moduli spaces of framed sheaves on surfaces

76%
Open Mathematics
|
2012
|
tom 10
|
nr 4
1455-1471
EN
We provide generalizations of the notions of Atiyah class and Kodaira-Spencer map to the case of framed sheaves. Moreover, we construct closed two-forms on the moduli spaces of framed sheaves on surfaces. As an application, we define a symplectic structure on the moduli spaces of framed sheaves on some birationally ruled surfaces.
10
Content available remote

On the Brill-Noether theory for K3 surfaces

76%
Open Mathematics
|
2012
|
tom 10
|
nr 4
1486-1540
EN
Let (S, H) be a polarized K3 surface. We define Brill-Noether filtration on moduli spaces of vector bundles on S. Assume that (c 1(E), H) > 0 for a sheaf E in the moduli space. We give a formula for the expected dimension of the Brill-Noether subschemes. Following the classical theory for curves, we give a notion of Brill-Noether generic K3 surfaces. Studying correspondences between moduli spaces of coherent sheaves of different ranks on S, we prove our main theorem: polarized K3 surface which is generic in the sense of moduli is also generic in the sense of Brill-Noether theory (here H is the positive generator of the Picard group of S). The harder part of the proof is proving the non-emptiness of the Brill-Noether loci. In the case of algebraic curves such a theorem, proved by Griffiths and Harris and, independently, by Lazarsfeld, is sometimes called the strong theorem of the Brill-Noether theory. We finish by considering a number of projective examples. In particular, we construct explicitly Brill-Noether special K3 surfaces of genus 5 and 6 and show the relation with the theory of Brill-Noether special curves.
11
Content available remote

Recent results on quiver sheaves

64%
EN
In this article, we survey recent work on the construction and geometry of representations of a quiver in the category of coherent sheaves on a projective algebraic manifold. We will also prove new results in the case of the quiver • ← • → •.
first rewind previous Strona / 1 next fast forward last
JavaScript jest wyłączony w Twojej przeglądarce internetowej. Włącz go, a następnie odśwież stronę, aby móc w pełni z niej korzystać.