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Enumeration of rational curves with cross-ratio constraints

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0 Published in 2017 at "Advances in Mathematics"

DOI: 10.1016/j.aim.2016.10.010

Abstract: Abstract In this paper we prove the algebraic–tropical correspondence for stable maps of rational curves with marked points to toric varieties such that the marked points are mapped to given orbits in the big torus… read more here.

Keywords: rational curves; cross ratio; marked points; curves cross ... See more keywords

A degree bound for families of rational curves on surfaces

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1 Published in 2019 at "Journal of Pure and Applied Algebra"

DOI: 10.1016/j.jpaa.2018.02.033

Abstract: We give an upper bound for the degree of rational curves in a family that covers a given birational ruled surface in projective space. The upper bound is stated in terms of the degree, sectional… read more here.

Keywords: rational curves; degree bound; families rational; bound families ... See more keywords

Wonderful compactifications and rational curves with cyclic action

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1 Published in 2022 at "Forum of Mathematics, Sigma"

DOI: 10.1017/fms.2023.26

Abstract: Abstract We prove that the moduli space of rational curves with cyclic action, constructed in our previous work, is realizable as a wonderful compactification of the complement of a hyperplane arrangement in a product of… read more here.

Keywords: wonderful compactifications; moduli space; cyclic action; rational curves ... See more keywords

Spaces of Low-Degree Rational Curves on Fano Complete Intersections

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1 Published in 2019 at "International Mathematics Research Notices"

DOI: 10.1093/imrn/rnz026

Abstract: In this paper, we prove that the moduli space of low degree rational curves on a low-degree complete intersection passing several suitable points is a complete intersection. The proof involves some relationships among some divisors… read more here.

Keywords: rational curves; curves fano; fano complete; spaces low ... See more keywords

Geometric Manin’s conjecture and rational curves

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1 Published in 2019 at "Compositio Mathematica"

DOI: 10.1112/s0010437x19007103

Abstract: Let $X$ be a smooth projective Fano variety over the complex numbers. We study the moduli space of rational curves on $X$ using the perspective of Manin’s conjecture. In particular, we bound the dimension and… read more here.

Keywords: rational curves; conjecture rational; manin conjecture; geometric manin ... See more keywords