Results 11 to 20 of about 306 (28)

Geometry of intersections of some secant varieties to algebraic curves

Journal of the London Mathematical Society, Volume 103, Issue 1, Page 288-313, January 2021., 2021
Abstract For a smooth projective curve, the cycles of subordinate or, more generally, secant divisors to a given linear series are among some of the most studied objects in classical enumerative geometry. We consider the intersection of two such cycles corresponding to secant divisors of two different linear series on the same curve and investigate the
Mara Ungureanu
wiley   +1 more source

Covering gonality of symmetric products of curves and Cayley–Bacharach condition on Grassmannians

Forum of Mathematics, Sigma
Given an irreducible projective variety X, the covering gonality of X is the least gonality of an irreducible curve $E\subset X$ passing through a general point of X. In this paper, we study the covering gonality of the k-fold symmetric product
Francesco Bastianelli, Nicola Picoco
doaj   +1 more source

Brill-Noether loci of pencils with prescribed ramification on moduli of curves and on severi varieties on $K3$ surfaces

Forum of Mathematics, Sigma
Under the assumption that the adjusted Brill-Noether number $\widetilde {\rho }$ is at least $-g$ , we prove that the Brill-Noether loci in ${\mathcal M}_{g,n}$ of pointed curves carrying pencils with prescribed ramification at the ...
Andreas Leopold Knutsen, Sara Torelli
doaj   +1 more source

Martens-Mumford's Theorems for Brill-Noether Schemes arising from Very Ample Line Bundles

, 2015
Tangent Spaces of V^r_d(L), Specific subschemes of C_d arising from various line bundles on C, are described. Then we proceed to prove Martense Theorem for these schemes, by which we determine curves C, which for some very ample line bundle L on C and ...
Bajravani, Ali
core   +1 more source

Special divisors on curves on K3 surfaces carrying an Enriques involution

, 2016
We study the pencils of minimal degree on the smooth curves lying on a K3 surface X which carries a fixed-point free involution. Generically, the gonality of these curves is totally governed by the genus 1 fibrations of XComment: 8 pages; simplified and ...
Ramponi, Marco
core   +1 more source

Gonality of modular curves in characteristic p

, 2006
Let k be an algebraically closed field of characteristic p. Let X(p^e;N) be the curve parameterizing elliptic curves with full level N structure (where p does not divide N) and full level p^e Igusa structure. By modular curve, we mean a quotient of any X(
Poonen, Bjorn
core   +1 more source

A family of irreducible free divisors in P^2 [PDF]

, 2014
An infinite family of irreducible homogeneous free divisors in $K[x, y, z]$ is constructed. Indeed, we identify sets of monomials $X$ such that the general polynomial supported on $X$ is a free divisor.Comment: comments are ...
Nanduri, Ramakrishna
core  

On the birationality of the adjunction mapping of projective varieties [PDF]

, 2011
Let $X$ be a smooth projective $n$-fold such that $q(X)=0$ and $L$ a globally generated, big line bundle on $X$ such that $h^0(K_X+(n-2)L) >0$. We give necessary and sufficient conditions for the adjoint systems $|K_X+kL|$ to be birational for $k \geq n ...
Knutsen, Andreas Leopold
core  

Focal schemes to families of secant spaces to canonical curves

, 2017
This article is a generalisation of results of Ciliberto and Sernesi. For a general canonically embedded curve $C$ of genus $g\geq 5$, let $d\le g-1$ be an integer such that the Brill--Noether number $\rho(g,d,1)=g-2(g-d+1)\geq 1$. We study the family of
Hoff, Michael
core   +1 more source

Remarks on syzygies of $d$-gonal curves

, 2005
We apply a degenerate version of a result due to Hirschowitz, Ramanan and Voisin to verify Green and Green-Lazarsfeld conjectures over explicit open sets inside each $d$-gonal stratum of curves $X$ with ...
Aprodu, Marian
core   +1 more source