Journal: Annali della Scuola Normale Superiore di Pisa, Classe di Scienze

Abbreviation

Ann. sc. norm. super. Pisa, Cl. sci. (Testo stamp.)

Publisher

Scuola Normale Superiore

Journal Volumes

ISSN

0391-173X

Description

Filters

2017 - 201912020 - 20254
Reset filters

Search Results

Publications 1 - 5 of 5
  • Enumerativity of virtual Tevelev degrees
    Item type: Journal Article
    Lian, Carl; Pandharipande, Rahul (2025)
    Annali della Scuola Normale Superiore di Pisa, Classe di Scienze
    Tevelev degrees in Gromov-Witten theory are defined whenever there are virtually a finite number of genus-g maps of fixed complex structure in a given curve class β through n general points of a target variety X. These virtual Tevelev degrees often have much simpler structure than general Gromov-Witten invariants. We explore here the question of the enumerativity of such counts in the asymptotic range for large curve class β. A simple speculation is that for all Fano X, the virtual Tevelev degrees are enumerative for sufficiently large β. We prove the claim for all homogeneous varieties and all hypersurfaces of sufficiently low degree (compared to dimension). As an application, we prove a new result on the existence of very free curves of low degree on hypersurfaces in positive characteristic.
  • Generic finiteness of minimal surfaces with bounded Morse index
    Item type: Journal Article
    Carlotto, Alessandro (2017)
    Annali della Scuola Normale Superiore di Pisa, Classe di Scienze
  • Non-orientable slice surfaces and inscribed rectangles
    Item type: Journal Article
    Feller, Peter; Golla, Marco (2023)
    Annali della Scuola Normale Superiore di Pisa, Classe di Scienze
    We discuss differences between genera of smooth and locally-flatnon-orientable surfaces in the 4-ball with boundary a given torus knot or 2-bridge knot. In particular, we establish that a result by Batson on the smoothnon-orientable 4-genus of torus knots does not hold in the locally-flat category.We further show that certain families of torus knots are not boundaries of embed-ded Möbius bands in the 4-ball and other 4 manifolds.Our investigation of non-orientable surfaces whose boundary is a giventorus knot is motivated by our approach to unify the proof of the existence of in-scribed squares and of inscribed rectangles with aspect ratio √3 in Jordan curveswith a regularity condition. This generalizes a result by Hugelmeyer for smoothJordan curves.
  • Gluing metrics with prescribed Q-curvature and different asymptotic behaviour in high dimension
    Item type: Journal Article
    Hyder, Ali; Martinazzi, Luca (2021)
    Annali della Scuola Normale Superiore di Pisa, Classe di Scienze
    We show a new example of blow-up behaviour for the prescribed Q-curvature equation in even dimension 6 , higher, namely given a sequence (V-k) subset of C-0(R-2n) suitably converging we construct for n >= 3 a sequence (u(k)) of radially symmetric solutions to the equation
  • Stratification and averaging for exponential sums: bilinear forms with generalized Kloosterman sums
    Item type: Journal Article
    Kowalski, Emmanuel; Michel, Philippe; Sawin, Will (2020)
    Annali della Scuola Normale Superiore di Pisa, Classe di Scienze
    We introduce a new comparison principle for exponential sums over finite fields in order to study "sum-product" sheaves that arise in the study of general bilinear forms with coefficients given by trace functions modulo a prime q. When these functions are hyper-Kloosterman sums with characters, we succeed in establishing cases of this principle that lead to non-trivial bounds below the Polya-Vinogradov range. This property is proved by a subtle interplay between etale cohomology in its algebraic and diophantine incarnations. We give a first application of our bilinear estimates concerning the first moment of a family of L-functions of degree 3.
Publications 1 - 5 of 5