1,721,003 research outputs found
A note on some moduli spaces of Ulrich bundles
No full textWe prove that the modular component M(r), constructed in the Main Theorem in Fania and Flamini (Adv Math 436:109409, 2024. https://doi.org/10.1016/j.aim.2023.109409), of Ulrich vector bundles of rank r and given Chern classes, on suitable threefold scrolls Xe over Hirzebruch surfaces F_e≥0, which arise as tautological embeddings of projectivization of very- ample vector bundles on F_e, is generically smooth, irreducible and unirational. A stronger result holds for the suitable associated moduli space M_Fe (r ) of vector bundles of rank r and given Chern classes on F_e, Ulrich w.r.t. the very ample polarization c_1(E_e) = O_Fe(3,b_e), which turns out to be generically smooth, irreducible and unirational
Hilbert schemes of some threefold scrolls over F_e
Full text linkHilbert schemes of suitable smooth, projective 3-fold scrolls over the Hirzebruch surface F_e, with e > 1, are studied. An irreducible component of the Hilbert scheme parametrizing such varieties is shown to be generically smooth of the expected dimension and the general point of such a component is described. This article generalizes the study of Hilbert schemes done in arXiv:1110.5464 for e=1
Cones of lines having high contact with general hypersurfaces and applications
No full textGiven a smooth hypersurface of degree , we study the cones swept out by lines
having contact order at a point . In particular, we
prove that if is general, then for any and , the cone has dimension exactly . Moreover, when
is a very general hypersurface of degree , we describe the
relation between the cones and the degree of irrationality of
--dimensional subvarieties of passing through a general point of . As
an application, we give some bounds on the least degree of irrationality of
--dimensional subvarieties of passing through a general point of ,
and we prove that the connecting gonality of satisfies
On complete intesections containing a linear subspace
No full textConsider the Fano scheme F_k(Y) parameterizing k-dimensional linear subspaces contained in a complete intersection Y in IP^m of multi-degree d = (d_1,....,d_s). It is known that, if t:= t(m,d,k) <= 0 and d_1....d_s >2, for Y a general complete intersection as above, then F_k(Y) has dimension −t. In this paper we consider the case t>0. Then the locus W(d,k) of all complete intersections as above containing a k-dimensional linear subspace is irreducible and turns out to have codimension t in the parameter space of all complete intersections with the given multi-degree. Moreover, we prove that for general [Y] in W(d,k) the scheme F_k(Y) is zero-dimensional of length one. This implies that W(d,k) is rational
Corrigendum to the paper "On the K^2 of degenerations of surfaces and the multiple point formula"
No full textWe correct an error in the Multiple Point Formula (7.3) in the paper mentioned in the title. This correction propagates to formulas (7.5), (7.6), (7.23) and (8.18), and it affects minor results in Section 8, where few statements require an extra assumption, but it does not affect the main results of Section 8
Lectures on Brill-Noether theory
No full textThese notes are the summary of lectures given by the author, in the framework of Joint Lectures of F. Flamini and E. Sernesi, at the Workshop
”Curves and Jacobians”, organized by the Korean Institute of Advanced Study (Seoul) and held on October 18-21, 2010, at Sol Beach Resort, Yangyang (Korea
A note on gonality of curves on general hypersurfaces
Full text linkThis short paper concerns the existence of curves with low gonality on smooth
hypersurfaces X in P^{n+1}. After reviewing a series of results on this topic, we report on a recent
progress we achieved as a product of the Workshop Birational geometry of surfaces, held at
University of Rome “Tor Vergata” on January 11th–15th, 2016. In particular, we obtained
that if X is a very general hypersurface of degree d grater than or equal to 2n + 2, the least gonality of
a curve C ⊂ X passing through a general point of X is explicitely given, apart
from some exceptions we list
Equivalence of families of singular schemes on threefolds and fourfolds
No full textThe main purpose of this paper is twofold. We first
analyze in detail the meaningful geometric aspect of the method
introduced in previous papers of the author, concerning
families of irreducible, nodal "curves" on a smooth, projective threefold X.
This analysis gives some geometric interpretations not investigated in the previous papers and
highlights several interesting connections with families of other singular geometric
"objects" related to X and to other varieties.
Then, we use this method to study analogous
problems for families of singular divisors on ruled fourfolds suitably
related to X. This enables us to show that Severi varieties of vector bundles
on X can be rephrased in terms of "classical" Severi varieties of divisors
on such fourfolds
On some sporadic moduli spaces of Ulrich bundles on some 3-fold scrolls over
Full text linkWe investigate on the existence of some sporadic , rank- Ulrich vector bundles on suitable -fold scrolls over the Hirzebruch surface , which arise as tautological embeddings of projectivization of very-ample vector bundles on that are uniform in the sense of Brosius and Aprodu--Brinzanescu. Such Ulrich bundles arise as deformations of ``iterative extensions by means of sporadic Ulrich line bundles. We moreover explicitely describe irreducible components of the corresponding sporadic moduli spaces of rank vector bundles which are Ulrich with respect to the tautological polarization on . In some cases such irreducible components turn out to be a singleton, in some other cases such components are generically smooth, whose positive dimension has been computed and whose general point turns out to be a slope-stable vector bundle.27 pages, submitted preprint; first author has been supported by PRIN 2017SSNZAW; second author has been partially supported by MIUR Excellence Department Project MatMod@TOV 2023-202
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