论文标题
第2属和第3属的d-椭圆基因座
d-elliptic loci in genus 2 and 3
论文作者
论文摘要
我们考虑了第2属和3属曲线的基因座，将$ d $ -to-1映射到属1曲线。通过可允许的封面压实这些基因座后，我们获得了其Chow类的公式，在$ d = 2 $时恢复了Faber-Pagani和Van Zelm的结果。答案表现出类似于固定属1曲线理论中的拟产性特性。我们猜想准地模性持续在较高的属中，并表明许多可能的变体。
We consider the loci of curves of genus 2 and 3 admitting a $d$-to-1 map to a genus 1 curve. After compactifying these loci via admissible covers, we obtain formulas for their Chow classes, recovering results of Faber-Pagani and van Zelm when $d=2$. The answers exhibit quasimodularity properties similar to those in the Gromov-Witten theory of a fixed genus 1 curve; we conjecture that the quasimodularity persists in higher genus, and indicate a number of possible variants.
