Results 21 to 30 of about 2,305 (55)

The Tate Conjecture for a family of surfaces of general type with p_g=q=1 and K^2=3

, 2015
We prove a big monodromy result for a smooth family of complex algebraic surfaces of general type, with invariants p_g=q=1 and K^2=3, that has been introduced by Catanese and Ciliberto. This is accomplished via a careful study of degenerations.
Lyons, Christopher
core   +1 more source

New building blocks for F1${\mathbb {F}}_1$‐geometry: Bands and band schemes

Journal of the London Mathematical Society, Volume 111, Issue 4, April 2025.
Abstract We develop and study a generalization of commutative rings called bands, along with the corresponding geometric theory of band schemes. Bands generalize both hyperrings, in the sense of Krasner, and partial fields in the sense of Semple and Whittle.
Matthew Baker, Tong Jin, Oliver Lorscheid   +2 more
wiley   +1 more source

Limits of special Weierstrass points

, 2007
Let C be the union of two general connected, smooth, nonrational curves X and Y intersecting transversally at a point P. Assume that P is a general point of X or of Y. Our main result, in a simplified way, says: Let Q be a point of X.
Cumino, Caterina, Esteves, Eduardo, Gatto, Letterio   +2 more
core   +1 more source

Relative and absolute Lefschetz standard conjectures for some Lagrangian fibrations

Journal of the London Mathematical Society, Volume 111, Issue 4, April 2025.
Abstract We show that the hyper‐Kähler varieties of OG10‐type constructed by Laza–Saccà–Voisin (LSV) verify the Lefschetz standard conjecture. This is an application of a more general result, stating that certain Lagrangian fibrations verify this conjecture. The main technical assumption of this general result is that the Lagrangian fibration satisfies
Giuseppe Ancona, Mattia Cavicchi, Robert Laterveer, Giulia Saccà   +3 more
wiley   +1 more source

Gromov–Witten invariants of bielliptic surfaces

Journal of the London Mathematical Society, Volume 111, Issue 2, February 2025.
Abstract Bielliptic surfaces appear as a quotient of a product of two elliptic curves and were classified by Bagnera–Franchis. We give a concrete way of computing their GW‐invariants with point insertions using a floor diagram algorithm. Using the latter, we are able to prove the quasi‐modularity of their generating series by relating them to ...
Thomas Blomme
wiley   +1 more source

ACM bundles on del Pezzo surfaces [PDF]

, 2009
ACM rank 1 bundles on del Pezzo surfaces are classified in terms of the rational normal curves that they contain. A complete list of ACM line bundles is provided. Moreover, for any del Pezzo surface $X$ of degree less or equal than six and for any $n\geq
Pons-Llopis, Joan, Tonini, Fabio
core   +3 more sources

On Weil–Stark elements, I: Construction and general properties

Journal of the London Mathematical Society, Volume 110, Issue 5, November 2024.
Abstract We construct a canonical family of elements in the reduced exterior powers of unit groups of global fields and investigate their detailed arithmetic properties. We then show that these elements specialise to recover the classical theory of cyclotomic elements in real abelian fields and also have connections to the theory of non‐commutative ...
David Burns, Daniel Macias Castillo, Soogil Seo   +2 more
wiley   +1 more source

L${L}$‐functions of Kloosterman sheaves

Proceedings of the London Mathematical Society, Volume 129, Issue 5, November 2024.
Abstract In this article, we study a family of motives Mn+1k$\mathrm{M}_{n+1}^k$ associated with the symmetric power of Kloosterman sheaves constructed by Fresán, Sabbah, and Yu. They demonstrated that for n=1$n=1$, the L$L$‐functions of M2k$\mathrm{M}_{2}^k$ extend meromorphically to C$\mathbb {C}$ and satisfy the functional equations conjectured by ...
Yichen Qin
wiley   +1 more source

Autoequivalences of blow‐ups of minimal surfaces

Bulletin of the London Mathematical Society, Volume 56, Issue 10, Page 3257-3267, October 2024.
Abstract Let X$X$ be the blow‐up of PC2$\mathbb {P}^2_\mathbb {C}$ in a finite set of very general points. We deduce from the work of Uehara [Trans. Amer. Math. Soc. 371 (2019), no. 5, 3529–3547] that X$X$ has only standard autoequivalences, no non‐trivial Fourier–Mukai partners, and admits no spherical objects. If X$X$ is the blow‐up of PC2$\mathbb {P}
Xianyu Hu, Johannes Krah
wiley   +1 more source