اشترك بالحزمة الذهبية واحصل على وصول غير محدود شمرا أكاديميا
تسجيل مستخدم جديدEnumeration of Genus-Three Plane Curves with a Fixed Complex Structure
143
0
0.0
(
0
)
تأليف
A. Zinger
اسأل ChatGPT حول البحث
ﻻ يوجد ملخص باللغة العربية
We give a practical formula for counting irreducible nodal genus-three plane curves that a fixed generic complex structure on the normalization. As an intermediate step, we enumerate rational plane curves that have a $(3,4)$-cusp.
قيم البحث
اقرأ أيضاً
We express the genus-two fixed-complex-structure enumerative invariants of P^2 and P^3 in terms of the genus-zero enumerative invariants. The approach is to relate each genus-two fixed-complex-structure enumerative invariant to the corresponding symplectic invariant.
Let $C$ be a smooth, absolutely irreducible genus-$3$ curve over a number field $M$. Suppose that the Jacobian of $C$ has complex multiplication by a sextic CM-field $K$. Suppose further that $K$ contains no imaginary quadratic subfield. We give a bo
und on the primes $mathfrak{p}$ of $M$ such that the stable reduction of $C$ at $mathfrak{p}$ contains three irreducible components of genus $1$.
We enumerate complex curves on toric surfaces of any given degree and genus, having a single cusp and nodes as their singularities, and matching appropriately many point constraints. The solution is obtained via tropical enumerative geometry. The sam
e technique applies to enumeration of real plane cuspidal curves: We show that, for any fixed $rge1$ and $dge2r+3$, there exists a generic real $2r$-dimensional linear family of plane curves of degree $d$ in which the number of real $r$-cuspidal curves is asymptotically comparable with the total number of complex $r$-cuspidal curves in the family, as $dtoinfty$.
We give a formula for the number of genus-two fixed-complex-structure degree-d plane curves passing through 3d-2 points in general position. This is achieved by completing Katz-Qin-Ruans approach. This papers formula agrees with the one obtained by the author in a completely different way.
This paper has been withdrawn by the author, due a crucial mistake in proof of lemma 4.2.
سجل دخول لتتمكن من نشر تعليقات
التعليقات
جاري جلب التعليقات
سجل دخول لتتمكن من متابعة معايير البحث التي قمت باختيارها
