Manuscripta Mathematica最新文献

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 obtain upper bounds for the torsion in the K-groups of the ring of integers of imaginary quadratic number fields, in terms of their discriminants.

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].

The shifting numbers measure the asymptotic amount by which an endofunctor of a triangulated category translates inside the category, and are analogous to Poincaré translation numbers that are widely used in dynamical systems. Motivated by this analogy, Fan–Filip raised the following question: “Do the shifting numbers define a quasimorphism on the group of autoequivalences of a triangulated category?” An affirmative answer was given by Fan–Filip for the bounded derived category of coherent sheaves on an elliptic curve or an abelian surface, via properties of the spaces of Bridgeland stability conditions on these categories. We prove in this article that the question has an affirmative answer for abelian varieties of arbitrary dimensions, generalizing the result of Fan–Filip. One of the key steps is to establish an alternative definition of the shifting numbers via bounded t-structures on triangulated categories. In particular, the full package of a Bridgeland stability condition (a bounded t-structure, and a central charge on a charge lattice) is not necessary for the purpose of computing the shifting numbers.

We provide a closed form expression for linear Hodge integrals on the hyperelliptic locus. Specifically, we find a succinct combinatorial formula for all intersection numbers on the hyperelliptic locus with one (lambda )-class, and powers of a (psi )-class pulled back along the branch map. This is achieved by using Atiyah–Bott localization on a stack of stable maps into the orbifold (left[ {mathbb {P}}^1/{mathbb {Z}}_2right] ).