Manuscripta Mathematica最新文献

Let (Omega ) be a domain on the unit n-sphere ( {mathbb {S}}^n) and ( overset{{,}_circ }{g}) the standard metric of ({mathbb {S}}^n), (nge 3). We show that there exists a conformal metric g with vanishing scalar curvature (R(g)=0) such that ((Omega , g)) is complete if and only if the Bessel capacity ({mathcal {C}}_{alpha , q}({mathbb {S}}^nsetminus Omega )=0), where (alpha =1+frac{2}{n}) and (q=frac{n}{2}). Our analysis utilizes some well known properties of capacity and Wolff potentials, as well as a version of the Hopf–Rinow theorem for the divergent curves.

In this paper, we give an affirmative answer to a conjecture of Collins-Yau [8]. We investigate the Chern number inequalities on 4-dimensional Kähler manifolds admitting the deformed Hermitian-Yang-Mills metrics under the assumption ({{hat{theta }}}in (pi ,2pi )).

On the free loop space of compact symmetric spaces Ziller introduced explicit cycles generating the homology of the free loop space. We use these explicit cycles to compute the string topology coproduct on complex and quaternionic projective space. The behavior of the Goresky-Hingston product for these spaces then follows directly.

We relate the mass growth (with respect to a stability condition) of an exact auto-equivalence of a triangulated category to the dynamical behaviour of its action on the space of stability conditions. One consequence is that this action is free and proper whenever the mass growth is non-vanishing.

Let ({mathscr {E}}) be a vector bundle on a smooth projective variety (Xsubseteq {mathbb {P}}^N) that is Ulrich with respect to the hyperplane section H. In this article, we study the Koszul property of ({mathscr {E}}), the slope-semistability of the k-th iterated syzygy bundle ({mathscr {S}}_k({mathscr {E}})) for all (kge 0) and rationality of moduli spaces of slope-stable bundles on Del Pezzo surfaces. As a consequence of our study, we show that if X is a Del Pezzo surface of degree (dge 4), then any Ulrich bundle ({mathscr {E}}) satisfies the Koszul property and is slope-semistable. We also show that, for infinitely many Chern characters (textbf{v}=(r,c_1, c_2)), the corresponding moduli spaces of slope-stable bundles ({mathfrak {M}}_H(textbf{v})) when non-empty, are rational, and thereby produce new evidences for a conjecture of Costa and Miró-Roig. As a consequence, we show that the iterated syzygy bundles of Ulrich bundles are dense in these moduli spaces.

In this paper, we obtain several characterizations of varieties of Fano type and projective spaces via absolute complexity. Also, we show that if the absolute complexity of a given pair ((X,Delta )) is negative, then the pair ((X,Delta )) does not admit any (-(K_X+Delta ))-minimal models.

We introduce an analogue to the amalgamation of metric spaces into the setting of Lorentzian pre-length spaces. This provides a very general process of constructing new spaces out of old ones. The main application in this work is an analogue of the gluing theorem of Reshetnyak for CAT(k) spaces, which roughly states that gluing is compatible with upper curvature bounds. Due to the absence of a notion of spacelike distance in Lorentzian pre-length spaces we can only formulate the theorem in terms of (strongly causal) spacetimes viewed as Lorentzian length spaces.

We give a precise estimate for the average scalar curvature of the Weil–Petersson metric on the moduli space ({overline{{{mathcal {M}}} }}_g) as (grightarrow infty ) up to the order (1/g^2).

We compute Hodge numbers and zeta function of a Kummer Calabi-Yau 3-folds introduced by M. Andreatta and J. Wiśniewski in [2] and investigated by M. Donten-Bury in [13].