On total reality of meromorphic functions

First steps towards total reality of meromorphic functions

It was earlier conjectured by the second and the third authors that any rational curve $g:{\mathbb C}P^1\to {\mathbb C}P^n$ such that the inverse images of all its flattening points lie on the real line ${\mathbb R}P^1\subset {\mathbb C}P^1$ is real algebraic up to a linear fractional transformation of the image ${\mathbb C}P^n$. (By a flattening point $p$ on $g$ we mean a point at which the Frenet $n$-frame $(g',g'',...,g^{(n)})$ is degenerate.) Below we extend this conjecture to the case of meromorphic functions on real algebraic curves of higher genera and settle it for meromorphic function…

关于亚纯映射与超曲面的一个新的退化第二基本定理

A new degenerated second main theorem for meromorphic mappings with hypersurfaces

本文为代数非退化亚纯映射与次一般位置超曲面族建立了带截断计数函数的第二基本定理，得到更优的总亏量上界，截断级别独立于超曲面数量，且仅需弱贝祖性质。

A generalized Quot scheme and meromorphic vortices

Let X be a compact connected Riemann surface. Fix a positive integer r and two nonnegative integers d_p and d_z. Consider all pairs of the form (F, f), where F is a holomorphic vector bundle on X of rank r and degree d_z-d_p, and f : {\mathcal O}^{\oplus r}_X \rightarrow F is a meromorphic homomorphism which an isomorphism outside a finite subset of X and has pole (respectively, zero) of total degree d_p (respectively, d_z). Two such pairs $(F_1, f_1) and $(F_2, f_2) are called isomorphic if there is a holomorphic isomorphism of F_1 with F_2 over X that takes f_1 to f_2. We construct a natural…

CM values of automorphic Green functions on orthogonal groups over totally real fields

Generalizing work of Gross--Zagier and Schofer on singular moduli, we study the CM values of regularized theta lifts of harmonic Whittaker forms. We compute the archimedian part of the height pairing of arithmetic special divisors and CM cycles on Shimura varieties associated to certain quadratic spaces over an arbitrary totally real base field. As a special case, we obtain an explicit formula for the norms of the CM values of those meromorphic modular forms arising as regularized theta lifts of holomorphic Whittaker forms.

认证投影的现实性

Certifying reality of projections

该研究利用牛顿不变集理论，开发了一种方法来认证多项式系统解的投影现实性，并应用于计算 genus 4 曲线的实和全实三切面数量。