Zobrazeno 1 - 10
of 19
pro vyhledávání: '"Eric Riedl"'
Publikováno v:
Forum of Mathematics, Sigma, Vol 12 (2024)
We study the enumerativity of Gromov–Witten invariants where the domain curve is fixed in moduli and required to pass through the maximum possible number of points. We say a Fano manifold satisfies asymptotic enumerativity if such invariants are en
Externí odkaz:
https://doaj.org/article/9895be8f2e6345cc98e0ddb057d72102
Autor:
Izzet Coskun, Eric Riedl
Publikováno v:
Proceedings of the London Mathematical Society. 125:1353-1376
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::57f7761947bc3ac0ac1bfd7137c95a93
https://doi.org/10.1112/plms.12484
https://doi.org/10.1112/plms.12484
Autor:
David Y. Yang, Eric Riedl
Publikováno v:
Journal of Algebraic Geometry. 31:1-12
In this paper we further develop a Grassmannian technique used to prove results about very general hypersurfaces and present three applications. First, we provide a short proof of the Kobayashi conjecture given previously established results on the G
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::4d060d80bb66d7d99c5fc71a73f6688a
https://doi.org/10.1090/jag/786
https://doi.org/10.1090/jag/786
Autor:
Eric Riedl, Roya Beheshti
Publikováno v:
Algebra Number Theory 14, no. 2 (2020), 485-500
Let $X$ be a very general hypersurface of degree $d$ in $\mathbb{P}^n$. We investigate positivity properties of the spaces $R_e(X)$ of degree $e$ rational curves in $X$. We show that for small $e$, $R_e(X)$ has no rational curves meeting the locus of
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::f6d1022431b21903c63a7c3f10ce73e3
https://doi.org/10.2140/ant.2020.14.485
https://doi.org/10.2140/ant.2020.14.485
Publikováno v:
Advances in Mathematics. 408:108557
We prove several classification results for the components of the moduli space of rational curves on a smooth Fano threefold. In particular, we prove a conjecture of Batyrev on the growth of the number of components as the degree increases. The key t
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::46a5380f3ceff02d7176376a3aa3db29
https://doi.org/10.1016/j.aim.2022.108557
https://doi.org/10.1016/j.aim.2022.108557
Autor:
Eric Riedl, Roya Beheshti
Publikováno v:
Duke Mathematical Journal. 170
Let $X$ be an arbitrary smooth hypersurface in $\mathbb{C} \mathbb{P}^n$ of degree $d$. We prove the de Jong-Debarre Conjecture for $n \geq 2d-4$: the space of lines in $X$ has dimension $2n-d-3$. We also prove an analogous result for $k$-planes: if
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::9277bbaba3cabc4ab05b6272ca81d410
https://doi.org/10.1215/00127094-2021-0035
https://doi.org/10.1215/00127094-2021-0035
Autor:
Eric Riedl, Izzet Coskun
Publikováno v:
Advances in Mathematics. 350:1314-1323
We prove that a curve of degree dk on a very general surface of degree d ≥ 5 in P 3 has geometric genus at least d k ( d − 5 ) + k 2 + 1 . This gives a substantial improvement on the celebrated genus bounds of Geng Xu. As a corollary, we deduce t
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::063a2a8e0e9d5235565862e4db4e7fb6
https://doi.org/10.1016/j.aim.2019.04.062
https://doi.org/10.1016/j.aim.2019.04.062
We study the space of rational curves on del Pezzo surfaces in positive characteristic. For most primes p we prove the irreducibility of the moduli space of rational curves of a given nef class, extending results of Testa in characteristic 0. We also
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::35bf1731da4d13bb0ac2004515e184fd
Autor:
Eric Riedl, David Y. Yang
Publikováno v:
Journal für die reine und angewandte Mathematik (Crelles Journal). 2019:207-225
We investigate the spaces of rational curves on a general hypersurface. In particular, we show that for a general degree d hypersurface in ℙ n {\mathbb{P}^{n}} with n ≥ d + 2 {n\geq d+2} , the space ℳ ¯ 0 , 0 ( X , e ) {\overline{\mathcal{
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::39e40c1fb0b5d6a097a33bdc660db9b5
https://doi.org/10.1515/crelle-2016-0027
https://doi.org/10.1515/crelle-2016-0027
Autor:
Eric Riedl, Izzet Coskun
We prove that a general complete intersection of dimension $n$, codimension $c$ and type $d_1, \dots, d_c$ in $\mathbb{P}^N$ has ample cotangent bundle if $c \geq 2n-2$ and the $d_i$'s are all greater than a bound that is $O(1)$ in $N$ and quadratic
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::6cf49d8487392aa05074d9df311e1b40
http://arxiv.org/abs/1810.07666
http://arxiv.org/abs/1810.07666