اشترك بالحزمة الذهبية واحصل على وصول غير محدود شمرا أكاديميا
تسجيل مستخدم جديدThe Computation of the Logarithmic Cohomology for Plane Curves
96
0
0.0
(
0
)
اسأل ChatGPT حول البحث
ﻻ يوجد ملخص باللغة العربية
We give algorithms of computing bases of logarithmic cohomology groups for square-free polynomials in two variables. (Fixed typos of v1)
قيم البحث
اقرأ أيضاً
We study the normal map for plane projective curves, i.e., the map associating to every regular point of the curve the normal line at the point in the dual space. We first observe that the normal map is always birational and then we use this fact to
show that for smooth curves of degree higher than four the normal map uniquely determines the curve. Our proof works in characteristic zero and in positive characteristic higher than the degree of the curve. We notice also that in high characteristic strange curves provide examples of different plane curves with same curve of normal lines. We will reinterpret our results also in the modern terminology of bottlenecks of algebraic curves.
We construct proper good moduli spaces parametrizing K-polystable $mathbb{Q}$-Gorenstein smoothable log Fano pairs $(X, cD)$, where $X$ is a Fano variety and $D$ is a rational multiple of the anti-canonical divisor. We then establish a wall-crossing
framework of these K-moduli spaces as $c$ varies. The main application in this paper is the case of plane curves of degree $d geq 4$ as boundary divisors of $mathbb{P}^2$. In this case, we show that when the coefficient $c$ is small, the K-moduli space of these pairs is isomorphic to the GIT moduli space. We then show that the first wall crossing of these K-moduli spaces are weighted blow-ups of Kirwan type. We also describe all wall crossings for degree 4,5,6, and relate the final K-moduli spaces to Hackings compactification and the moduli of K3 surfaces.
Let $X$ be a complex analytic manifold, $Dsubset X$ a free divisor with jacobian ideal of linear type (e.g. a locally quasi-homogeneous free divisor), $j: U=X-D to X$ the corresponding open inclusion, $E$ an integrable logarithmic connection with res
pect to $D$ and $L$ the local system of the horizontal sections of $E$ on $U$. In this paper we prove that the canonical morphisms between the logarithmic de Rham complex of $E(kD)$ and $R j_* L$ (resp. the logarithmic de Rham complex of $E(-kD)$ and $j_!L$) are isomorphisms in the derived category of sheaves of complex vector spaces for $kgg 0$ (locally on $X$)
There are no known failures of Bounded Negativity in characteristic 0. In the light of recent work showing the Bounded Negativity Conjecture fails in positive characteristics for rational surfaces, we propose new characteristic free conjectures as a
replacement. We also develop bounds on numerical characteristics of curves constraining their negativity. For example, we show that the $H$-constant of a rational curve $C$ with at most $9$ singular points satisfies $H(C)>-2$ regardless of the characteristic.
We prove the universal triviality of the third unramified cohomology group of a very general complex cubic fourfold containing a plane. The proof uses results on the unramified cohomology of quadrics due to Kahn, Rost, and Sujatha.
سجل دخول لتتمكن من نشر تعليقات
التعليقات
جاري جلب التعليقات
سجل دخول لتتمكن من متابعة معايير البحث التي قمت باختيارها
