ترغب بنشر مسار تعليمي؟ اضغط هنا

On the Brill-Noether loci of a curve embedded in a K3 surface

91   0   0.0 ( 0 )
 نشر من قبل Luigi Pagano
 تاريخ النشر 2018
  مجال البحث
والبحث باللغة English
 تأليف Luigi Pagano




اسأل ChatGPT حول البحث

We slightly extend a previous result concerning the injectivity of a map of moduli spaces and we use this result to construct curves whose Brill-Noether loci have unexpected dimension.



قيم البحث

اقرأ أيضاً

We compute the integral cohomology groups of the smooth Brill-Noether varieties $G^r_d(C)$, parametrizing linear series of degree $d$ and dimension exactly $r$ on a general curve $C$. As an application, we determine the whole intersection cohomology of the singular Brill-Noether loci $W^r_d(C)$, parametrizing complete linear series on $C$ of degree $d$ and dimension at least $r$.
In this paper we consider the Brill-Noether locus $W_{underline d}(C)$ of line bundles of multidegree $underline d$ of total degree $g-1$ having a nonzero section on a nodal reducible curve $C$ of genus $ggeq2$. We give an explicit description of the irreducible components of $W_{underline d}(C)$ for a semistable multidegre $underline d$. As a consequence we show that, if two semistable multidegrees of total degre $g-1$ on a curve with no rational components differ by a twister, then the respective Brill-Noether loci have isomorphic components.
144 - Eric Larson , Hannah Larson , 2020
Let $C$ be a curve of genus $g$. A fundamental problem in the theory of algebraic curves is to understand maps $C to mathbb{P}^r$ of specified degree $d$. When $C$ is general, the moduli space of such maps is well-understood by the main theorems of B rill--Noether theory. Despite much study over the past three decades, a similarly complete picture has proved elusive for curves of fixed gonality. Here we complete such a picture, by proving analogs of all of the main theorems of Brill--Noether theory in this setting. As a corollary, we prove a conjecture of Eisenbud and Schreyer regarding versal deformation spaces of vector bundles on $mathbb{P}^1$.
117 - Olivier Benoist 2017
We show that the set of real polynomials in two variables that are sums of three squares of rational functions is dense in the set of those that are positive semidefinite. We also prove that the set of real surfaces in P^3 whose function field has le vel 2 is dense in the set of those that have no real points.
Consider a smooth projective 3-fold $X$ satisfying the Bogomolov-Gieseker conjecture of Bayer-Macr`{i}-Toda (such as $mathbb P^3$, the quintic threefold or an abelian threefold). Let $L$ be a line bundle supported on a very positive surface in $X$. If $c_1(L)$ is a primitive cohomology class then we show it has very negative square.
التعليقات
جاري جلب التعليقات جاري جلب التعليقات
سجل دخول لتتمكن من متابعة معايير البحث التي قمت باختيارها
mircosoft-partner

هل ترغب بارسال اشعارات عن اخر التحديثات في شمرا-اكاديميا